V nekaj trebih lektur. Vsega lektura dobro je zelo, da je zelo, da je zelo, da je zelo. Neliko nismo tudi nekaj, da je v USA, vsega je v Bostonu, in da se dobro v Bostonu dobro. Zato smo vsega izgledali na nekaj prezentacij, prezentacije kvantumov, ki so pričo se zelo vsega vsega vsega vsega vsega vsega vsega vsega. Zelo vsega vsega vsega vsega in vsega vsega vsega vsega, So systems that you can. Think of a similarity to the Keep advice type of modeling in the context of others classical systems. Of course you do a quantum treatment it will be slightly different so you will have to do with matrices and okay this is something you will see je veliko zelo svobodno, veliko zelo svobodno, ali se vseč je vseč samo. Zato videljš, da se vseč zelo sega in zelo sega in tudi v kvantumih modelji zelo sega vseč vseč vseč vseč vseč vseč vseč vseč vseč vseč vseč. Vseč videljš vseč vseč vseč vseč vse je, da je zelo način, je zapravil v trajne, zelo v teželnih zelo, na tessin, kaj je. Vse je, da je vse izgleda, vse je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, v kratom verju. Zato to je vse objev, zato način... Vsih je mnoj različ, če je zelo in najboljših vsega vzela in vsega vzela, da sem tudi vsega. To je produk na moj interaktivne... Vsega vsega vzela... Ivan Latela ki je tudi v Barcelonau. Zdaj smo začali kolaboracijo 6-7 rov. Zdaj to je nekaj nekaj kolaboracijo, tako, da je vzvečal v zelo, v zelo, da je vzvečal vzvečal vzvečal vzvečal vzvečal vzvečal vzvečal vzvečal vzvečal. Počučali smo se vzvečal, da smo zelo vzvečali o zelo, da smo vzvečali, da je vzvečal še je vzvečal vzvečal v zelo, z vzvečal vzvečal vzvečal. I ino nekaj, ovečal, če bo se vzvečal... OK. Zazvo so imamo vseč, očini vzvečal, je to, Prvno je to druga leksu, ali včetno ne bomo vsega leksu, ker je to pričo, da je bilo vsega leksu, tako sem spliti vsega leksu v 1a in 1b, je to vsega leksu, tako v 1a in 1b. In potem, okej, vsega leksu, This is a sixth lecture if you count properly the number of sessions that we have had. So, I'll go backward to the first lecture today. With concepts related to aditivity and long range interactions. But I will discuss these topics in a wider sense, in a thermodynamic sense. Čutko, zelo vši tudi, da bomo vzela vzela termodanamik. Vzela, da termodanamik je to vzela in je izvedne značno. Zato je tudi počkaj, da je vsečo informacije na sistem, in potem, da je vsečo, da je vsečo, da je vsečo, da je vsečo, da je vsečo, da je vsečo, da je vsečo, As in as, as you will see how it's possible to see the counterpart in stat mech. And so today will be devoted to the introduction of a new ensemble that maybe you never heard about. It's an ensemble where the number of particles fluctuates, the number of the energy fluctuates in volum je lažen. Tudi tudi tudi tudi lažen. Zdaj sem si, da je odvržal, da se zelo tudi tudi tudi lažen in tudi je vsega dobro. Zelo ne zelo tudi tudi lažen, ki se tudi tudi tudi lažen. In rezoj je, če pri svoj počet, that if the interactions, this was done by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by by. Long ago in the thirties that if the three quantities fluctuate all together, there are no equilibrium states. ta bilomče ne zelo učnično. Ne zelo je nekaj, da vse zelo vse začela, ta če je na štahla, nekaj nezelo je začela. Vse boče ne zelo vse začela, boče ne je začela. Taj je začelo učnične zelo. Zelo je zelo se vsega, zelo je začelo na tudi, ovo je nezelo, je začelo na zelo, zelo je začelo na zelo. Zelo je začelo na zelo. A termodynamic system. If the interactions are long range, there can be equilibrium states. Not only there can be equilibrium states I will show today a model that besides having equilibrium state, it has phase transitions and also phase transitions and phase diagrams are in equivalent in se prav ed ali oset. To je nov je gener� голoba, taآo se naj 말� Oke in sp auton in sağuj se, da sočil nam se izcušno poelo tje vone, nosimo in constranje na ne večske z coinšli iz UP. V pripad sac to zestaj vstavum odz fewerc There are profound things, I think about this aspect that the long range interactions allow this new ensemble. I would say that, as a suggestion to understand why this ensemble exist in long range interactions, you can think that usually what you have to do when you have a gas, you have to put a gas in a volume. In vseč, da jih se vseče, da se vseče. Vseče, da se vseče in energije. Sistemovati in vseče in vseče in vseče in vseče in vseče. zelo počkaj je zelo počkaj, ki ne počkaj vzela izgledaj. Vzelo počkaj je zelo prijevno v vse. To je nekaj ideja. Zelo je to izgledaj, da se počkaj počkaj počkaj ne vse odgledaj. Ok, zelo to je več intuitujivo, je zelo, da se taj vse, je vse objezena bilo, taj nekaj terasti. A potem, zelo, da selamo dolje stručno vzelo do modu, da je zelo vsevajal V70-i, z Valter Tilling. In, da je zelo, ta ljubov, zelo, da sem počutila v slaku, nekaj pačen počutih, ker sem nekaj počutil, da je problem, kaj je zelo, v 70-jih, in je problem nekaj negativne spesivne kete, in je korekli, da se počuti, zelo, da je problem v kontekstu, zelo, in vzelo, in zelo, in zelo, in zelo, in vzelo, vzelo, in vzelo, ki se zelo, da je zelo, in vse in zelo, kanoniko in mikrokanoniko in in in in in in in in in constreniko in zelo. In so, so je to več semplj modern, in je to, da je to, da je to, da je to, da je to, da je to informacija. In dan, in dan, In počim bomo izgledati, kako vso nerevnačne simulacije v tem nekaj nesemboljo, načo je montekarlo, ovo je radišljeni na toh nekaj nesemboljo. To je zrp. Zabijam tudi, kako najčešte, kako izgleda na 2015. Začnem način. As you know, as you have known, the additivity is a basic property of systems with short range interactions. It implies that energy. Let us look at additivity in a different way. Instead of looking at additivity as a property of the energy itself, let us put it in relation with the homogeneity of thermodynamic potentials. This is another way to look at additivity. In this new sense, additivity implies that energy is a linear homogenous function of entropy, volume and the number of particles. By the way, the property that you use when you derive the thermodynamic relations that imply energy, entropy, volume and number of particles. For instance, the way you write the work as in the so-called TDS equations, I used to call them in this way, but I will repeat this scaling property in a while so you will see where I use the additivity. As we have seen, the systems with power-low decaying interactions are non-additive. If the power alpha is smaller or equal than the dimension d of the embedding space. In fact, we have not seen many cases in which alpha equals d. It is a sort of limiting case. It is an interesting one, for instance, dipolar systems. There are many examples in physics, self-gravitating systems, Coulomb and dipolar systems, but also two-dimensional fluids like the atmosphere. There are plenty of applications in this field of the tool that we have learned. The non-additive interaction lead to ensemble in equivalence, which implies negative specific heat, temperature jumps, broken ego DCVs. There are plenty of new phenomena, quasi-stationary states, plenty of new phenomena that arise in this field. Just to put it in context, let us think how Gibbs introduced the so-called grand canonical ensemble. The idea of Gibbs is that it costs energy to change the number of particles. So you have a system and Gibbs thought of copies of the system, several copies of the system that are distinguishable, but they can have different number of particles. And having or not having a certain number of particles costs energy. OK, now let us generalize Gibbs idea. Now you have copies of a system that is long range. Each of the system is long range. And it can have a certain number of particles, a certain energy, a certain entropy. And you are making copies replicas of this system. And each of the system has n particles, energy, entropy s, and volume v. What changes in this game? Julio, could you please switch off your mic? So this was my glasses. Julio, Tani, Raffelli. OK, thank you. Switch off everything. So the only thing that varies is the number of copies. So the total energy will be the number of copies times the energy of a single system. The total entropy will be the sum. There is no interaction among the copies. It is like in the Gibbs construction. There is no interaction between copies of the grand canonical. So the construction is very similar, in fact, to the construction of Gibbs. So the total volume will be the total number of electrons times the volume of the single system. The total number of particles will be the number of volume. So now, OK, so this is very much inspired. I advise you to read the work of this guy, Hila. So the idea of Hila was different, but is very much connected with this one. So instead of creating copies of the system, he subdivides a single system, which is interacting in parts. And in fact, the name that he gives to this energy is the subdivision potential. So you can write a thermodynamic relation for the total energy, which includes the variation in the number of copies. OK, you see that it comes after the Gibbs term. So the variation of the energy of the total energy might be due to a variation of the entropy, TDS, to a variation of the volume minus PdV. For historical reason, there is a minus here. It depends on the sign of the work. Then the Gibbs variation, which is the chemical potential times the variation of the number of particles in a single system, plus a term, which takes into account the number of copies that might cost energy. OK? So we will see in a very simple way that in the case in which each single system is additive, the cost of adding a copy is zero. While if each single system is long range, is a bit magic, if each simple system is non additive, then it will cost energy to add the copy. So let's do it. So the proof is two lines. So you change the number of copies by factor xi. In such a way that the entropy is divided by factor xi, the volume is divided by factor xi, and the number is divided by factor xi. And is n total. OK, so is the n total. You do this on the total quantities. Then, of course, you just apply these relations, and you see that if you do like this, the variation of the entropy of the volume and of the number of particles is zero. And this implies that if this is zero, or this is zero on the right hand side, there is a direct relation between the variation of the total energy and the variation and the replica energy epsilon. Capital E. OK. But in additive systems, the energy is a linear homogeneous function of the entropy. So the energy of the system two is nothing but the energy of the c. So you see that I have to divide by factor xi. And therefore, dT is zero, which implies that E must be zero. So if the energy is a linear homogeneous function of its arguments, the replica energy is zero. But we know that for long range systems this is not true. So there must be an energy associated with the fact that you add a copy to the system. Let me move my. OK. So now you have to work a little bit with thermodynamics. So this is the integration of the equation for fixed single system properties. So I fix the numbers in the single systems. And just one step, you prove this relation. So if you divide by the number n of systems, you get this explicit relation that relates the energy, the entropy, the pressure and the volume and the replica energy. You have to do it to be convinced that it is OK. OK. So I put all the ingredients to do it. Then you differentiate this relation. And you take into account, go and look in a book of thermodynamics to the first TDS relation, to the first TDS equation. And you get an equation for the variation of the replica energy. OK. This is a relation that appears in thermodynamics book. It's called the Gibbs-Duhem relation. And you see that usually this Gibbs-Duhem relation has a zero on the left side, which implies that you cannot fix temperature, pressure and chemical potential independently. They are related by an equation of states in additive system. But here, because of long range interaction, you have an extra term, which is due to the variation of the energy associated to the variation of the number of copies. So the Gibbs-Duhem relation is violated. So this is one news. The Gibbs-Duhem relation, which usually takes for granted in thermodynamics book, is violated, but simply because in thermodynamics, you assume that the system is additive. If the system is non-additive, the Gibbs-Duhem can be violated. Moreover, if you integrate this equation, you can get an equation for E. So if you are able to compute, sorry, for calligraphic key for the replica energy, so if you are able to compute in a given ensemble for a given model, you are able to compute the thermodynamic functions and the equation of state, then you can write explicitly what is E. So it's not mysterious, this E, you can compute it. So the first thing that we did, and I will not repeat the historical steps, was to compute this E, this calligraphic E, in several different cases. So take a system in beam field and with decaying interaction, compute E. Or take the tilling model and compute E, for instance, in the microcanonical ensemble, since the model was solved in the microcanonical ensemble. So we took some time to familiarize, maybe you will see in the papers, but I don't want to follow the historical thread because it will be too long. So the procedure will be slightly different, more logical. So after we convinced ourselves that this E was calculable on some models directly, we started to think in a different way. And this different way is, since the kibs needed a new ensemble to formulate the problem of changing number of particles, there should be an ensemble that takes into account the variation in the number of copies. And this ensemble is this one, it's very simple to write, in fact, is a probability distribution, where you have three Lagrange multipliers, one for the number, one for the energy, and one for the volume. So there is no mystery in that. And then the corresponding partition sum is a partition sum where you have to, here the energy is discrete, but you can replace the sum over the energy states by an integral over the energy, of course you can replace the sum over the volume, everything in the continuous limit will be replaced by this. And so then the change in average energy can be written, you know that the expression has a change in the probabilities, in the usual way that you do for ensembles. Ja, so the index i runs over the copies on the replicas, right? The index i is the energy states. You don't see here the replicas, you see the single state, ok? You see the single, this is the probability distribution of the, ok. So this can vary, ok, the probability distribution of the single state and the variation induces a variation in the energy. So now I rewrite the variation in the energy using the conservation of probability and I obtain a relation, this relation where and bar v bar are the average number and the volume. And this is to be compared with this thermodynamic relation, ok? Which now allows to identify the thermodynamic functions so you can write the temperature in terms of the multiplier beta, the pressure, in terms of the multiplier gamma and beta and the chemical potential in terms of the two multipliers. And this is the entropy associated with this construction. So then substituting this relation in the expression for the probability in the entropy you get the expression of the replica energy. This is where the replica energy enters, ok? So from the thermodynamic relation for the replica energy and having computed these averages and the entropy I can obtain the replica energy which is nothing but as usual for the other ensemble which is nothing but kbt times the logarithm of the partition sum for this ensemble, ok? And by differentiation one obtains the relation for the replica energy so you can see that in this ensemble the entropy is minus the derivative of the replica energy with respect to temperature at fixed pressure and chemical potential the volume is the derivative of the energy of the replica energy with respect to pressure at fixed temperature and chemical potential and the number of particles you fix the other two. So you fix two over three and you get the fluctuating the average fluctuating quantities, ok? So this is the construction it is, ok? And of course there are legend transforms to the other ensembles so I can write the partition sum in one constrained ensemble for instance in terms of the partition sum in the ensemble in which temperature, volume and number of particles are fixed by simply legend transforming with respect to this would be the canonical ensemble, no? This is the canonical ensemble by legend transform with respect to the number of particles and with respect to the volume and obtain the partition sum in the unconstrained ensemble ok, this would be the canonical partition sum but I could also obtain it from the grand canonical partition sum which is this horrible symbol here by legend transform by laplace transforming with respect to by laplace transforming with respect to the pair, pressure and volume, ok? So I have several ways of deriving this new partition sum and this is a graph where I show all the ensembles that we could construct by this type of construction so I start for the entropy with the entropy which is the thermodynamic potential in the micro canonical ensemble where the energy, the volume and the number of particles are fixed, ok? Now I can let the energy fluctuate and I get the massier potential or the free energy if you want in the canonical ensemble in this construction as you have seen I am losing the invertibility of the Legend-Fenzhel transformer so there can be response functions that have not the right sign and in this case the response function which can be negative in the micro canonical ensemble but the more the yapmış polishive invariant the more specific it is which is the response function with respect to the energy so the variation of the temperature the variation of the energy with respect to the temperature the inverse of the variation of the temperature with respect to the energy in the micro canonical ensemble while it's variation of energy izgledajte vse rešvene v te dve odgledaj. V ena odgledaj je tudi vse poslutne. Tudi je to izgleda, kaj je tudi saj vse zelo. Zelo je to izgleda, da je vse izgleda, da je izgleda, da je izgleda, zato je zelo stabilitave, da se izgleda, in nekaj zaštej entropi, in tudi smo očetili tako, ok? Dakle smo očetili tvoj problem, da smo videli mnogo modelov, in da smo vedeli toga način, in bojte je tobe v tem, ok, no, there are two possible ways, Either, you free the volume, OK. Ida jih vse bolj, in jih jih vse prešel ensambolj, ko je to, ko je ensambolj, ko je komis, ko jih jih vse bolj, da je fizicist, ker vse vse način je konstant atmosferične prešelje, OK, zato... In ensambolj, ko je fizicist, to je najbolj vse, fizicist kaj je z komisem, z komisem. Zato se vzicega vzicega vzicega vzicega, vzicega vzicega vzicega. Zato vzicega vzicega vzicega. I je inovojnje obrženje, ko je kompresibilit, ki je nekaj negativ vzicega kanonima, in to, da je vsečo pozitiv na izobariče, v izobariče assembling. Kako ti različi, in je ideti v to, da bomo so vzlizili na izobariče in ovorili, kjer lahko tega vsečje. To je na začinaj izobariče ensambo, je mikro kanonika. Vseč je vsečč, energij, voliume in delenje partijov. Na izobariče, Or, you go to the grand canonical, where you let the number of particles fluctuate, and you have another associated, now I don't remember the name of this response function, but you have another associated the response function in which you can, that is necessarily positive in the canonical ensemble and can be negative in the grand canonical ensemble. Is the response associated with the fluctuations of the number of particles. Now, the two lines join in this new ensemble, so if you let in the grand canonical fluctuate the volume, then you reach the unconstrained, or the alternative, you let the number fluctuate in the isobaric, you let the number fluctuate in the isobaric, and you reach the unconstrained, which for massier potential has better times the, it was a bit lengthy, but this is the panorama that we have in front. So, and all types of inequivalences could be checked at any of these steps. So, there are models in which you can check inequivalence at any step when you release a quantity that is fixed in one ensemble. So, today we will concentrate on the new inequivalences that arise because of the existence of this new ensemble. So, the inequivalence, for instance, of the unconstrained ensemble with the isobaric ensemble. And in order to do that, I need the model, which is adapted for fluids. No, yes, so these inequivalences are always associated with the first order, first transitions in all these cases. Yes, yes, you need, so, yes, in general, yes. I would say that this general feature is that the associated thermodynamic function should have a region of where it is with a supporting line, with a supporting line. So, there should be an unconcavity of one thermodynamic potential and this can appear only at first order phase transition, not at second order phase transition. Do you have coexistence essentially? Yeah, you must have coexistence, a region of coexistence of the two phases, yes. I have no general proof of that, but this is what is, should happen in all these steps, yes. And also in the example that I will show today, it is like that. Okay, so, I think now it is clear and it is even very general what I have shown now. You see, general, so, if you have questions on that because I will now go to the model. No, everything clear? Yeah, it's a bit shocking the fact that you have this new thing. So, even for us it was not easy to accept that we had confinced ourselves. Okay. No, I was just wondering because when we spoke previously about replicas in all other courses, where when we were averaging over disorder and we would take the copies of the system with different realizations of disorder. So, I was wondering if this is like the underlying mechanism behind this, or this has nothing to do. No, no, we didn't have a good name for these copies. We call them replicas, Gibbs called them copies. So, we decided to call them replicas, but they have nothing to do with the problem in random systems. These are distinguishable copies of the same systems. This is the definition of a replica. Okay. Okay. So, now, let us go to a model that I like a lot. It was proposed by Walter Thiering. And in a paper that appears, and I have the copy that I will put on the web, is a certain preprint, and I like very much this paper. It's very well written. And it starts by asking how can be that specific heat is negative, and then, okay, it's a bit lost in the beginning. So, it starts by trying to average the... So, the issue was raised by Lynden Bell and Wood in a paper in 1966. And there was no answer to this issue, and the statistical mechanics community was sort of skeptic about the fact that an astronomer was questioning the basics of statistical mechanics by saying that specific heat could be negative. So, they were a bit suspicious that this guy, although he was a famous astronomer, he became a professor in Cambridge and one of the most famous astronomers in these years, so maybe he was a little bit too arrogant to say things that statistical physics community didn't like. But Thiering had the right attitude. So, he tried to understand. So, in the first part of the paper, he tries to do a trick to deal with gravity, with Newtonian gravity. And the trick was sort of like the entropic construction that we've seen in the Lynden Bell paper. The trick was sort of averaging over boxes. So, he was taking the system and then was trying to have an idea what happens if you average over boxes, and he gets a formula at the end of his first paragraph where a very complicated formula that he can rewrite. So, his objective was, of course, to compute the entropy and his idea from the start is very clear that he was thinking to ensemble in equivalence. So, that the only way out of this dilemma put by Lynden Bell was understanding what happens for thermodynamic entropy, for micro canonical entropy. So, he was pointing to the inequivalence of ensembles from the start. But then in the second paragraph of the paper he says, okay, I have all these boxes, but what if I replace by just one box? So, and that's very simple. It's a fantastic idea because everything is clear and you compute it into lines. So, you have a system now, it's put in a box, okay. You need a box. At that time, of course, people wanted the box because with gases it was like that. So, it doesn't work any... Okay, yes. So, and you have kinetic energy and you have potential energy and the potential energy essentially counts the number of particles that are in the inner box. The number of particles that are in the inner box means that if you have a pair of particles that are in the V0, in the volume V0, which is contained in the volume V, smaller than the volume V, then if they are together, they interact and they attract each other with a strength minus nu, okay. So, this is the theta function, is the theta function of the volume V0 and if the position of the particle is in the volume V0 and also the other particle, the particle i and the particle j must be in the volume V0, then they attract with a potential phi. If one of the particles is in the volume V0 and the other is outside, it doesn't count any energy of interaction, they are free to move and if both are out, they don't interact, okay. So, then I will finish the lecture by showing the entropy and the free energy of this model, but okay, so the total potential energy in the large and limit is just minus nu and zero square. So, you just count the number of particles that are in volume V0. Okay, so that's the problem and you have to solve the micro canonical entropy. Now, I leave it to you because from the knowledge that you have of counting with the spin models that we have seen and so I give you just two steps. First you have to do the integration over the momenta, which is easy to do. So, you write the delta and you integrate over the momenta is a Gaussian integral so you can do it and then you are, you have to do the integral over the positions. Okay, but the integral over the positions it is very simple because you have to integrate over the position dq1, dqn over the particles and particles can be only in volume V0 and in volume V0 and in volume. So, essentially there will be, so, okay. So, you have to remember that you have to, this is, so, okay, you have to integrate some integrant after having integrated over the momenta and so the count, the relevant counting factor is n factorial divided by n0 factorial, which is the number of particles in the volume V0 and n minus n0 factorial. This is the relevant counting factor. Now, this n factorial will be killed by the Gibbs paradox factor that you put in the omega. So, you remain with that and then you have to maximize with respect to n0. So, you count all states. So, you have to count all states irrespective what is in the zero value. And there you use the saddle point. No, you have to maxima at large n. You have to, so, you use the steering approximation and you do the large n. It's really very simple. You get the results and these are the parameters as a tilling we're putting them. So, this is the number of particles, the ratio of the number of particles that are in the gas phase. So, 1 minus n0 over n. So, these are the number of particles that are in the gas phase. This is the rescaled energy. So, since the energy in this model is growing like n square and there has not been, yes? Yes, sure.  In the previous slide, like in the definition of the Hamiltonian. Why we don't divide by n0 square here? No, no, by n0 in the definition of the Hamiltonian for the interaction term. Ah, yes, yes. So, this was the time in which they were not using the cut-series scaling. So, I do it naively as they were doing. Very good question. In the cut-scaling, so the system is fine at n for the moment. And in fact, if you do the thermodynamic limit without doing the cut-scaling, you run into troubles. And what Turing did was to define the energy in a different way. So, it defines the energy divided by n square and then it divides the temperature divided by n. And in this way, n is intensive, ok, and the energy also is intensive. And the reason of this plus one is that in this way all the energies are positive in the model. Ok, it's just a normalization. So, it's a different scaling, but it is equivalent to the cut-scaling in the end. Ok. It could have done introducing the cut-scaling Thank you for the question. It was a bit sloppy. And this parameter eta is very interesting because for some reason he likes this logarithm of this because in the previous calculation he had a ratio between the volumes that was exponential of some function. So then it calls the scaling factor for the volume. He calls it exponential of this, he was calling it f, but f makes confusion with the free energy so we decided to call it eta. But these are exactly the parameters that he used in this scale. Then, if you do this integral there, you get this entropy which is the the fraction of the number of gas of this expression. You see that again this entropy has some fermionic flavor through this term and this is the part coming from the kinetic energy. So this entropy does not have the decreasing part that we have seen in spin systems. It is an entropy of a gas essentially, of an interacting gas. So if you put more energy in the system the energy which is not taken by the potential energy will be taken by the kinetic energy. So the volume will keep increasing as you put more energy. So the entropy will never decrease. So it will always increase. It is a generic feature of a system with kinetic energy. It is the first one that we see in fact. So it is important to you could check for instance that if you define a micro canonical temperature using this expression for the entropy there is no negative temperature region. So this is even more clear because sometimes you could tend to associate the negative specific heat without negative temperature. This is a system without negative temperature. So all temperatures are positive for all the states. Nevertheless, the specific heat can be negative. And then you have canonical free energy which is as you see I have to divide the free energy and take the inf. So essentially this is the legend-fenchel transform of the canonical free energy. A plot, unfortunately I wanted to add a slide on this, but OK, the original slide, but I take it from a paper that we wrote recently. So we realize a couple of years ago that no one had computed the phase diagram of the model. So we decided to compute the phase diagram of the model and the situation of ensemble in equivalence that appears here is again associated with the first-order phase transition which is different in the two ensembles. So you see that in the OK, tau is the rescaled temperature. Tau is the rescaled temperature. So I'm plotting the phase diagram in the two variables that rescaled temperature and the parameter eta. And I can compute the critical point in the two ensembles by expanding, by using a Landau expansion in the order parameter which is the fraction of the volumes. So the order parameter is the density in this case. And if I use the variables adapted to the canonical so the intensive variable adapted to the canonical ensemble, I get a line of first-order phase transition with the end point which is here which is a second-order phase transition in the canonical ensemble. And if I do it in the micro-canonical exactly you remember the area that was at the form of a fish in the models that we have solved, spin models. In this case is this area here which are states that are not accessible in the micro-canonical ensemble. And in fact if you cross these, so for instance at fixed temperature you cross this area here there is a jump in etha. I remind you etha is essentially the log of the fraction of the volumes the external volume v0 is a parameter of the Hamiltonian you have to think of v0 as a parameter of the Hamiltonian while the volume is the volume containing the gas which is fixed. When I take the thermodynamic limit I let the volume increase with the number of particles that increase in such a way to have a constant density but v0 is a parameter of the Hamiltonian. By the way there is a very interesting limit that you could do is when you take the volume to infinity you could take the volume v0 to 0. And in this case because you go back to a short range interacting system. So v0 is a sort of finite in the in the larger volume limit. So it's affecting a finite part of the system and this also is one of the ingredient of the in equivalence in this in this model. If you want this is a modern way of looking what Tiring was looking. Tiring was always putting himself in this region so he had a jump in density and a jump in temperature and he was never looking at the full phase diagram. We decided to look at the full phase diagram and the full phase diagram is the following. So you have a critical point which is not the same in the two ensembles as for the Blumechappel model and for the they don't agree the two in this case is the critical point. So we have to solve the discussion at that point because coming also to the question of Matteo. So where I should expect ensemble in equivalence near first order phase transition. Now in this case the first order line is not the same you can see but there is no tri-critical point in this model so there is no region of second order and first order transitions. There is a line of first order transition in both ensembles that finishes in the critical point but the positions of the two lines and of the position of the critical point are not the same. So that creates the ensemble in equivalence. So the phase diagram is intrinsically different in this ensemble. Ok, so this is if you want the first part of the lecture I took one hour and in the second part I will show the application of the formalism of the unconstrained ensemble to the theory model. Now the problem that we had when we tried to apply the unconstrained to the theory model the theory model is not rich enough to create states in this new ensemble equilibrium states in this new ensemble. So we were very depressed because we were convinced that there were states in this new ensemble but we could not find them with the theory model. So you will see that the trick was to enrich the theory model to put if you want unphysical pressure from outside. So besides attracting the particle v0 you push the particle that are outside into the volume v0 then you get equilibrium states. So the model was not rich enough in parameters in order to give equilibrium states in this new ensemble. I think if you take other models you have to play with parameters in such a way that you get is not for given that you get a new ensemble. But we were expecting them and you have to modify the theory model in such a way to allow a richer. We were looking for phase transitions and I remember I gave a talk two years ago in Buenos Aires before the pandemic and I put the question to the audience we could find equilibrium states but we could not find phase transitions and then when we started to discuss these then the idea was to put the particle with an excluded volume. So the final step is to have a theory model with an external pressure plus a size for the particle. And if you put all them together then you get everything. Equilibrium points, phase transitions and ensemble in equivalence. So you have to sort of enrich the model. So just to see what do you mean is are you changing the Hamiltonian? Not changing the Hamiltonian. So by this pressure term how do you change the Hamiltonian? You will see. I add a term in the potential energy I will do it explicitly I add a term in the potential energy which introduces a pressure from outside. I have to change the Hamiltonian So if I study this model in the unconstrained ensemble I don't get equilibrium states. So if you want to get a picture it's like thinking of these particles inside an inflated balloon which lives in a system with pressure peak. Yes. Yes. I don't know how physically it can appear but okay. It's an unphysical modification. Without V0 this is an ideal gas, right? It's an ideal gas. It exerts pressure on or even say on a free piston. You could think also if one does a sort of repelling particle so in some sense the particle should attract when they are in V0 and should repel when they are in V1. This would be also analog. So they are not free particles? No. Even when they are in V1. So here they are free particles when they are in V1. In the T-ring model they are free particles. But when they are in V1 they repel. If they are in V0 or they repel if they are in V1. How to do this? I don't know because they are the same particles. Why they should repel in V1 and attract in V0. So one could think for instance of shining a laser in the inner part in order to change the sign of the interaction among the particles. Particles that naturally would repel if you shine a given region then they should attract. This would be the physical way of I have no idea. It's totally unphysical. But one has to think of a way of realizing this. I think in social interaction it's easy. So either you like each other or you don't like each other.  I think it's a non-physical system and it's easy to think. Just to finish I think the idea of tearing I find it very interesting and I think he is a pioneer in this solution of the problem. Although people attribute these to others like Lynden Bell and others. But I think this paper by tearing is really the corner point in the solution of the puzzle. And this model that I am doing in the last lecture should have been in the first lecture. But for logical reasons it's better to introduce somebody in equivalence in spin models that are models of magnetism that are more easy to solve in some sense and more familiar to us. But I think this model is a really fantastic way and is the solution of the puzzle put by Lynden Bell in 66 with finding the By the way I knew a personal story I met tearing several times and I have been honored to serve in the committee of the Erwin Schrodinger Institute in Vienna that he created and he was an amazing person so I remember once during dinner for his celebration of maybe he was 80 or something like that he said in physics I tried I tried in physics always to find confirmation of something and I always found a contradiction so also this way of thinking is very interesting so you can work to confirm a basic thing but he was saying that in trying to confirm something you find a contradiction that leads you to another direction so I think it was a very interesting lesson also and he has several examples of this kind in his papers where if you look in detail what the theory that you have you discover aspects that at the first sight you neglected and they are important and this leads you to new directions of investigations unfortunately this paper in 1970 remained a sort of unknown for several years I think we discovered it at the end of the 90s it was a sort of unknown ok, 5 minutes of break then we hope to finish at one so we take 5 minutes break recording stopped if you take the ensemble if you take the ensemble at constant pressure so we start again hello so we start again thank you recording in progress sorry it was a problem with the microphone sorry I forgot the microphone so I repeat there is an extra term which is a repulsion in the volume maybe I am wrong here I don't remember so I have to check the sign but I'm sure it is a repulsion for the case in which we have states and then we ok so so this is the modified theory model in one dimensions in two dimensions and in three dimensions so particles have the sides v1, repel and they attract in the volume v0 so this is more or less the picture so then I compute the canonical partition sum already till indeed and then by Laplace transforming by Laplace transforming I get the unconstrained partition sum so I have to solve this problem here it's not difficult to solve I do it as usual with the Laplace method so and unfortunately there is one aspect it is technical but it is important that the volume I've told you that the volume of tilling is this one you see that it's ok, this is now explicit this is the integral that you see on the blackboard the integral over the positions divided by the Gibbs factor combinatorial factor it's a sum over n0 and n1 with the constraint that n is the sum of n0 and n1 so there is a chronicle delta here and then the tilling in the tilling case there is no sigma so it's v0 to the n0 v1 to the n1 divided n factorial ok but in the case in which there is a sigma in which there is a size for the particles the the expression is correct only in one dimension so there are corrections in dimension 2 and dimension 3 so in fact when we published the paper we were not aware of this difficulty we were not expert enough of question of state for systems of so now we have a paper that we are preparing that corrects this mistake in this paper so ok so this is the the first time you see an expression so this is the replica energy at volume v0 volume v and with a certain number of particles is the explicit expression of the replica energy and here k is a sum over 0 and 1 ok there are 2 containers either you are inside v0 outside v0 and there is an explicit formula for the you can compute then you use the steering approximation then you do the saddle point so large n and you get the replica energy and the replica energy function of the thermodynamic parameters of the system so is like the entropy the free energy is so it would be 0 if the system were additive and clearly this system is not additive because the energy goes like n square so the system is not additive and so you get a finite a finite thermodynamic potential epsilon in order to express this thermodynamic potential in terms of the 3 parameters that now fix the state of the system so the which are pressure chemical potential and temperature you have to solve in this set of consistency equation so you see that they are implicit because you see that temperature appears here for instance so you have to invert you have 3 equations and 3 unknowns so you have to invert in mu p t as a function of the averages because here everything fluctuates so the volume fluctuates so so you have an average volume the number of particles fluctuates so you have an average number of particles both in the inner part and in the outer part and you get them as a function of tp and mu for instance when sigma equals 0 we get these we get these and it's very interesting the form that is taken by by the replica energy is minus the potential plus pv so if you go and look at the thermodynamic relation you see that it is related to the thermodynamic relation that we wrote in the first part of the talk so we have also sort of reasoning where we we take the excess part of this quantity with respect to short range so in some sense there is a long range contribution to the pressure this part of the pressure that come from the gas but what appears in this relation is the pressure due to the long range minus the pressure which is due to the standard short range gas so this you can see in these expressions so it's a long and tedious work to do so we have a long paper about that here I essentially recall some result so equilibrium configuration so for sigma equals zero so when the particle do not have a size like in the theorem model equilibrium configurations exist in the unconstrained ensemble only if b is negative so for repulsive interactions for b equals zero which is the theorem model no equilibrium states exist in the unconstrained ensemble and then there are other functions for instance the unconstrained ensemble are equivalent when b is negative in the grand canonical ensemble equilibrium states exist also for b positive so also when both are positive so when you have both attractions in the two regions and some of these states have negative isothermal compressibility this is one of the response functions that can be negative no phase transition is present in the canonical ensemble the grand canonical ensemble is inequivalent to the canonical ensemble and in this lateral ensemble so in the canonical ensemble phase transition of first order critical point is present in analogy with the theorem model and moreover negative compressibility states appear in the canonical ensemble also for b negative so there are different behaviors in the isothermal now that we have a very complicated set of ensembles we can check several properties and they are different in the different ensembles depending what choice of parameters you do all that for sigma zero sigma non zero as I have said is correct in one dimension so so we introduce a new set of variables which because in this case we have a and b so slightly different from the set of variables that theorem has so adding a feature and then we have so we have a different form of so this is the replica energy it is scaled also for sigma positive and the new feature is that with sigma positive you get phase transitions for instance here is a first order phase transition I am now plotting this function which is unusual free energy so it is a free energy that does not exist for system with short range interactions and here I show that by varying one parameter I have one case in which a minimum is here at these values of x zero which is the fraction of rescaled fraction of particles that are in the box v zero the minimum is here so I have a state here and this is a metastable state and if I change a parameter in this case psi I don't remember one of the rescaled parameters maybe the chemical potential I go from this minimum here to this minimum here so I have a phase transition of first order by varying one parameter and it can be very complicated so you see here the space of parameter is larger so this is the analogous of the opening of the of the forbidden phase in the plane that will not now appear in the space because I have more parameters so it is slightly difficult these are this gray surface there the limits the region in this three-dimensional space where I can have states below on the other side of the gray surface I don't have states there are no equilibrium states on the left side there are equilibrium states and there is a line in the unconstrained ensemble of second order phase transition with two surfaces and the upper surfaces and the lower surfaces the limit region where there are no states so you have jumps if I vary for instance if I vary x bar in the in the vertical direction at some point I have a jump like temperature jumps this type of discontinuities that we have seen in the simpler models it's a richer situation, a richer model this is for instance an example of in equivalence of isothermal isobaric with unconstrained in the isothermal isobaric I have a line transition ending on to a critical point in the case of the unconstrained I have a line I have a spinode line one could call it a line which delimits states that do not exist in this ensemble and finishes on a second-order critical point so I have a very unusual situation and this is something like a cut in the previous three-dimensional plot so I'm cutting a specific region of these are really details so I could give other details of these models and this is very recent so this is the example how you do simulation in this system you need to reservoir one for the particles and one for the volume and then it's simply Monte Carlo acceptance and probabilities for configurations so you have to move the particles around and then compute the acceptance rate according to how you vary the energy and here the energy is more complicated so the energy is the replica energy so you have to count in a new way but is a standard Monte Carlo so now for instance here is a simulation where we don't put the inner volume V0 doesn't exist particles only repel and they stay in volume V0 so particles stay in volume V0 and they only repel and there are equilibrium states and we reach this equilibrium state with Monte Carlo very precise do you see so these are the lines that these models can be easily solved one is one in the class of theory models and it's easily solved and then we compare the analytical solution with numerical simulation and this is a rather different case in which now uncomparing isothermal and isobaric there is a side for the particles now and there is repulsion and you see that you have a typical situation of inequivalence so in one ensemble I follow the line and I reach metastable states and then I have a region of inequivalence because this quantity cannot increase in one ensemble while in the unconstrained I have a first order first order phase transition in the unconstrained the maximum construction that you have seen in the in the first lectures so as usual when you go in an uncharted region you try to explore so we are continuing the exploration of these different models in this uncharted region of the theory model but of course one could try also with other models and also more realistic models so in these lectures I have tried to convey the idea that in long range interactions we have a new ensemble which can have equilibrium states phase transitions like the other ensembles we are calling this ensemble the unconstrained ensemble the terminal potential for this unconstrained ensemble is the replica energy the replica energy can be computed explicitly even analytically in some models I have not shown but it can be computed also for one over r to the alpha interactions in the mean field approximation and the unconstrained ensemble can be equivalent to the other ensembles but cannot also so there are cases of inequivalence and ok, this is just an exploration that is going on we are now using equations of state for fluids in two and three dimensions to correct the the solution that we have published which is valid only in one dimension and that's all I think since this is my last lecture I think you can leave it open for discussion and if you have also questions to put on previous previous lectures starting from tomorrow Nikolaj Defeno will give lecture on the quantum quantum mean field is in model ok questions? don't be shy anyhow you will be here I will be here tomorrow and I'm available for you will do the teaching assistant I will do the teaching assistant I will try to reproduce the calculation of Nikolaj because some of them I don't fully control because I'm not so I don't know much about quantum systems but I wanted to give a flavor of with these three more lectures all these things are being now exported to the quantum domain finding fish that are similar fish that are new so it's interesting ok, so I think we can close here and have lunch so, thank you again


Welcome traders to this week's live market and trading analysis session with me Patrick Monthly. I'm going to be providing some insight into the E-mini S&P 500 today as we head into the cash open for New York trading. Before we get started here, obviously want to adhere to risk disclaimers. Views and opinions expressed by me are solely mine, they're not indicative or representative of those held by Tickmill UK and Tickmill Europe Limited and obviously trading carries inherent risk and you should assess your personal risk file before getting involved in the markets. So we're going to get going here in just a couple of minutes. I'm going to start off with a recap of the overnight session. I'm going to look at the trade plan heading into the cash session, identify some trade levels. I'll update you on my perspective and we'll go through the live action during the the open here and see if we can identify any asymmetric trading opportunities. Any questions you have feel free to type them into the chat. We've got a chat on Trading View and I'm guessing we probably have a live chat on the YouTube stream as well. So if you want to post questions into either of those chats, I'll jump back to them as and when I have chance during the session or at the end of the session depending upon how the action unfolds as we get going here in just over 10 minutes for the opening of the New York Stock Exchange. Okay, let's start with a recap of the overnight action before we get started actually. Just for those of you who aren't involved in the Facebook group, in partnership, exclusive partnership with Titmil, I run a strategy group, trading group, focused on futures options, forex, most markets really, and I provide daily updates, observations through the main page here as you can see. We get institutional insights and various technical observations. I provide trade setups, trade analysis, market analysis, all via this main page. But more importantly, the Titmil trader chat you can see here, you can join that once you access the actual group. This is more of a real-time environment where I post my ongoing market observations throughout the London and the open of the New York session, provide real-time trading updates, trade plans, institutional research from some of the major investment banks, which gives you a perspective on how the bigger players are positioned. I refer to it really as market intelligence as opposed to anything that you're going to immediately action, but it's really useful to have a gauge of how the bigger players in the market position because essentially as retail traders, what we're trying to do is ride the coattails of these bigger players and grab some of the meat of the move that these larger funds and trading desks are predominantly driving. So feel free to request access to the main page and then you can also access the trader chat. Let me just turn down this wire service in the background here one second. Okay, let's take a look at the trade planner from this morning to get a sense of the levels we're watching. So obviously we've got options expiration tomorrow, Friday, and I don't tend to be particularly active during options expiration. We obviously get some pre-erratic price action more often than not around that time and technical levels tend to be less adhered to. Certainly not as much on the monthly option expiry, which obviously we've got tomorrow, more around the quarterlies when you really get that impact in terms of options positioning and market makers and dealers trying to hedge out their risk. So coming into today's session we are long to neutral against this weekly bull bear zone. The bull bear zone that I am using for this week is the 4760 to 4770. Now yesterday we traded below there, we traded down to the 4740s coming just shy of the 4740 test before getting an impulse off the lows into the close last night. I did highlight to the guys in the room in the strategy group, sorry, that as we traded into that 4740, 4730 area, especially if it was late in the day I was going to be watching for a reaction there to engage on the long side. I got filled on a long through 4765 last night, managed to get half my position off plus five, so I'm risk free essentially long from 4760. Then coming into the London session today, I highlighted the potential for some resistance to come in around the 4790, 4795. That was via a voice note that I posted into the Tick-Mill Trevor chat. So guys in the group had advanced warning at that level and I watched for the reaction we got post the jobless claims where we tagged that 4795, we exceeded it by a couple of ticks and I played the reaction there off that level for a short, got filled at 4790. Again got half my position off risk free, so currently I'm running a long from 4760 which is risk free and a short from 4795 which is risk free. Now with these positions, I'll be watching for signs as we head into the cash session for one of those positions to be invalidated and then I'm going to be looking to add to the trade that that is working and at this stage my focus is on the long side. So I'll be looking for a breakthrough at 4795. The Clobex highs 47, just below 4798 and through the 4805 level to look to play long positions up, targeting a test of the expected range resistance today which actually comes in, that level on the 4801 is our expected range resistance. So if we can get through that 4801, then what I'm going to be watching for is using the market internal indicators to confirm that we have bullish momentum across the board and then we're going to be looking to add to those long positions. The target on the upside then is going to become the 4832 which is a two sigma standard deviation to the upside versus last night's closing price and technically more often than not, 95% of the time actually statistically speaking, when we test that 40, that two standard deviation move to the upside so the 47, the 4832 is 95% of the time, the market will actually close below that level and so if we pay close attention, if we get to that 4832, obviously 4825 has been significant resistance and those 4830s have held on numerous tests this year, but if we get a break there then we're going to be starting to take a look at the 4850s, 4860s and the 70s and I'll update you as to the levels if that plays out. Now the downside scenario is we start to get acceptance back below the 4780, the 4780, 85 level is this is today's current intraday ball bear zone. Let's move actually to the charts here so you can see this is a multi-time frame view, we've got the hourly chart here at the top left, four hour chart with the trade levels marked on so you can see I'm just shy of that 4801 daily projected range resistance, we've got daily projected range support down to that 4740, if we take out the 4740 on the downside 4710 should see a test and again that's a two-sigma move to the downside where once again we will be looking to play a potential counter trend long depending on the price action. So let's move to the intraday chart so this is my trading setup for the cash session, you can see this chart to the left is a five-minute chart and this is the one-minute chart, I use the one-minute chart specifically for the entity cases, the market internal tools that I use, this top pane here will be populated with what's called the TIC, the TIC highlights in every one minute iteration the amount of stocks on the New York Stock Exchange ticking up versus those ticking down, we have extreme areas that we monitor and when we trade towards this red zone so that's a thousand TICs on the upside, more often than not that will signal a pause in the move to the upside potential profit taking, a lot of programmatic trades use the TIC for profit taking and can if we're trading into one of the predefined supported resistance areas can actually act as a potential trade signal for me and vice versa on the downside of trading into the green zone here that's telling me that at least a thousand stocks on the New York Stock Exchange are ticking down as an extreme where we can see some programmatic profit taking so take less attention to the TIC and the trend I'll highlight that as we get going once it starts to populate above there we have the breadth indicator so the breadth is telling us the amount of volume the money flow into stocks going up versus stocks going down when we're when we're getting prints above the zero level that suggests there's more money going into stocks that are trading to the upside than there is to the downside vice versa when we are below the zero level that's a bearish reading suggesting more money is actually flowing into the stocks that are trading down versus those trading up and gives a bearish confirmation the top pane here is the AD line the advanced decline line so that's telling us how many stocks are advancing versus stocks declining and again trading above the zero level is bullish more stocks advancing on New York Stock Exchange than declining trading below the zero line is is a negative read and suggests bearishness so I use these these indicators or these market internals as to give me a read underneath the hood of the of the action that we're seeing at an index level when I refer to the index level obviously is the S&P 500 is the index the futures are derivative and the readings that we're getting from these market internals are actually telling us more specifically what's having happening at a stock level so at the constituent level of the S&P 500 so if the market is if the price action is moving to the upside or we're advancing but the breadth of the AD line are negative and that's telling me that underneath the hood there is there's a problem with the current trend and we're likely to see the potential for a reversal in the market the last tool I use and the one I refer to pretty regularly here is Delta market Delta so without going into too much detail here just as we're heading into the open Delta is essentially a reference to buying and selling pressure so if price is trending to the upside we want to see the Delta making new highs as a confirmation of the strength of the trend if we are seeing price move into highs as we saw with the spike here into that 97 25 in the pre-market you'll note that we didn't get a new high in Delta here we actually got what I referred to as Delta divergence so price made a new high we didn't get a new high in the Delta and that was my signal for the short trade that I'm currently in so I'll refer to Delta divergence regularly throughout the sessions over the weeks as we go ahead and you should be able to pick up what it is or how it is I use the tool but it really is a fantastic tool for confirmation or non confirmation of moves combined with the other market internals so we're a minute out from the open here and let's see where we where we open up and then I'm going to update trade levels what I'm using at the moment as we head into the cash trading session the blue and the gold line on here on the five minute chart represents the halfway back for the current trading session and the volume waste average price that's the blue line for the the current trading session that we have since the futures reopened last night in New York so so again I reference those as school session mid full session bwap and we use those throughout the session as reference points and certainly on pull backs they're very useful in confirming trends at the moment we are trading below the the daily five-period look back volume waste average price now this is key for me as it defines the the trend on the higher time frame and you'll notice here although these on a normal candlestick chart price moving to the upside we see green candles minor current colored red because we are trading below that that daily trend reference point which is 47.95 at the moment and so just to help me with with just an easy visual of where we are in the markets I have those colored with the trend for those who are in the strategy group you you can access these these indicates and my specific chart setup I share that with I can share that with you on personal request through the through the chat group so markets opening up we are positioned bullishly above the 47.80 and what I'm watching for now is as we open up let's see how these internal shape up we're getting a nice push higher here in terms of the one-minute market delta and we are trading above the full session mid full session bwap so for now the focus is to is to the upside for me personally what I'm obviously looking for is if my stock gets taken at the 47.95 that's going to be that's going to position me to the long side and I'm going to be looking for opportunities to add to my my long from 47.65 which is risk free versus 47.60 so let's see let's let these opening rotations go through and then we will we'll see where we are any questions like I say feel free to type them into the chat box and as and when I will I'll get to them as as timely fashion as possible market action allowing so we are seeing a positive ad line although we're pulling back off the opening prints here we have a positive breadth and tick opened up and an extreme obviously given the the overnight move that we've seen it's a it's a bullish reading on tick so we let the opening rotations go through to let the the internal settle out and see what we're looking for is an opening swing reference so we we opened up in that 47.86 we have the these two green lines that you can see forming here on the minute chart they are used for reference points for the initial balance measurement the initial balance is the opening hours range of price action because that has the the opening the iB high or the iB low are our reference points as the the day's trading continues so once we get through that opening hour those areas certainly if we're trending pullbacks to the iB high connect to support pullbacks to the iB low if we're trending to the downside connect to resistance and also we have a use for the the initial balance in terms of days when we gap up or gap down in terms of price because statistically there's a hyperability scenario that if we gap up and we don't we don't test the halfway back of the gap in the overnight session the gap from the close of the prior day and we break the iB high that's what we call a gap and go trade and those can be again really useful trading tools on on trending days obviously we we have opened with a small gap to the upside here at at the moment versus yesterday's settle price so we have a half gap let's draw that in so we've tested overnight we've traded in so the half gap comes in at 4782 and traded there yet in the full session now like i say because the gap versus last night's settle is is just about 10 points i prefer to trade the gap and go trade we like to see gaps that are bigger than 10 points to give a a decent signal but we do have that gap so watching for that that gap area 4782 to get filled we have just below the full session full session vwap so those are going to be some initial key references to suggest strength in this in this recovery to the upside but as as highlighted before in terms of the higher timeframe we have traded into the high volume on the alley timeframe 4792 trend channel resistance and currently have been rejected and hence the current short exposure that i'm running versus my my mom from yesterday's close so if we can get some if we can get a break of this 4800 4801 which is the anticipated range resistance for the day so if we can start to establish some value above there then what we're going to look for are these internals to be trending to the upside and we're going to be looking to play continuation trades so we look for a break consolidation and and then we look to play the break of that consolidation with the current trend to the upside i would highlight for trades my initial risk on any trade automatically through my automated trade management software means that i have a 10 point stop and that initial 10 point stop is equal to 1 percent account equity that's my pa account i obviously manage external capital as well and i have a reduced or a five more conservative risk exposure on that but personally i allocate an initial 1 percent risk and i look for more often though i'm looking for a five point move in favor of my trades to take off half that risk and reduce my exposure and then i use that five points that i've taken as a buffer for any pullbacks to my entry point especially when i'm playing continuation trends because we're playing breaks of resistance more often than not you get that well there is a tendency obviously to retest resistance as support but when markets really move you don't get those pullbacks that's why i play the continuation trades um given depending upon the the market structure and environment we're in and certainly if we start to take out that uh that hourly trend line uh trend channel resistance through the 4800s through the 4885 then we're looking at 10 15 and 24 and our two standards deviation resistance today comes in at 4832 on on the upside so those are going to be my immediate upside targets if we if we can hold the full session mid and full session b right before a for an upside extension here the alternative scenario is that we trade back down through the gap we take out the full session mid full session b wap and we uh we take another look at the 4770 from the upside now if uh if that plays out that's going to be to my mind first signal that we the elongs are in trouble and we could be seeing another leg to the downside and that then will set up those downside targets that i reference in the pre-market here we have 14 at the moment so we have uh we've traded just shy of the half gap versus that uh that 67 settle yesterday so we haven't tested the half gap yet so we're seeing the uh the ad line pullback breadth is around the zero line at the moment so no strong signal from the internals and that as you can see is replicating the price action we're going nowhere fast at the moment and uh i would highlight as well obviously we have options expiration tomorrow on Friday so it's likely that market makers are going to want to try and pin the price action to the uh the highest volume strike which i imagine is uh is somewhere around the 4800 level i'll actually drop you somewhere some confirmation on that let me see in any questions feel free to type them into the chat okay so no uh no tests so far back into that uh that half gap so this is suggesting we're we're getting some upside momentum developing here or energy building for the upside but we're not getting any confirmation from price as such at the moment so as we uh as we continue to trade uh within this opening swing TSNA has the recent index rate nine cycles that i think are actually released they're the only second right are filming in the planes i was thinking the delta starts are all over here we're pulling back uh from that 4790 let's see if uh if bids develop here into the half gap 4782 where we've got that full session mid and full session vwap sitting just above there so that's the confluence for um where you'd expect buyers to sit back in if we are going to make a make a move higher here the red gold and green lines you can see here this is the value area low for the current sessions that represents the base of 70 percent of the price action from the overnight session and so that's that's a key reference point 4775 the gold line represents the highest volume node for for the current session 4786 and the red area the red line represents the top of the 70 percent of the overnight volumes that's 4797 so those are the key reference points for then keeping an eye on throughout the day as uh as the volume profile builds currently you can see clearly we've got two distributions and up on a lower distribution we take out the lower distribution so it certainly shifts to the potential for downside price discovery at the moment like i say we're holding this key areas 4782 4780 as support for now no uh no real meaningful excursions away from that area currently for mexico which is written supporting must take a long at someone's the mexico city okay here we are 4783 tested just another 4782 you can see the blue line represents the volume based average price you're watching for bids to develop here what's the tick you're looking for strong tick prints here to suggest volume moving in uh to uh two shares ticking higher as we test those key reference points a lot of algorithms and programmatic trading models for uh large investment banks or trading desks use the volume based average price for the day as a reference point of value if they're having to execute big block orders for clients clients be watching um for that volume wasted average price as a reference point for where their trades are filled to represent that they're getting good value from their their execution desks and so if we uh if we're going to make we're going to make a strong push for the upside what we're looking for on this initial test back into the volume wasted average price you can see overnight we basically rotate it around it using it as support and resistance throughout overnight session and we're now looking as we head into cash session our first clue as to whether buyers are in control is going to be can we defend that full session mid full session vwap and uh i'll make a move higher here let's see oh in terms of the mag seven we've only got tesla and there's some pressure here 215 i'm currently running along in tesla from 218 using a 211 stop at the moment okay so there's the um the bid that's come in initially to defend the full session mid full session vwap to that 4780 has acted as initial support now see if we can take out the ibe high here as the as the next reference point to uh building building positivity here so the current ibe high of 4791 47975 so we need to see a move through there now to start to get this momentum going to the upside uh breadth is uh is neutral really and the ad line although positive is trending down from its uh from its opening print so again some big signals at the moment hence we're seeing some chop some heavy rotation in and around these uh this 4780 4790 so nothing to do at the moment waiting for uh running for a clear signal we've got a tick that is just between the uh plus 400 negative 400 print now tick is good also for confirming chops so when we're in that uh that plus or minus 400 zone that's uh that's suggesting just rotation for now not seeing any uh any meaningful trend developing the tick and certainly once if we do move out of this current ibe at the 4780 4790 want to see the tick start to move with that price trend has again there's a confirmation so it's really one of the key aspects of trading in the new session is this idea of being able to use these market internals as fantastic confirmation tools for your trades and certainly the more familiar you become with them and and and understanding how i think you know there is their movements as a reflection of the individual stocks feeding into what we're getting in terms of an index level movement you can really use them to your advantage and certainly i have for uh for a career that has now spent over 15 years again any questions feel free to type them into the chat boxes and uh and i'll get to them as and when a little bit more pressure coming in here on the downside we're seeing uh the delta start to to roll over a little bit here seeing that tick you see that push down in the tick you're seeing there at the moment now that's uh that's weighing on the market which as i said the breadth the top pan this pain here although open positive we are trending to the downside at the moment and sorry the ad line trending to the downside and we have breadth now that is just going a touch negative here so this is a bit of a concern here for um for the longs and we have now filled the half gap so uh that gap and go trade that i referenced at the beginning of the session the break of the ivy high is is no longer valid now as we've traded the half gap uh during the um the initial balance session so that trade is is off the table for me now but we are uh we're still holding in and around support we just want to see these internals improve here we'll start to pick up if we can if we can catch a uh a bit as uh as we test support for the seven eighties we've got all the uh the mag seven now in positive territory so for those who aren't familiar with the mag seven days these are the seven bigger stocks uh on the stocks exchange at the moment apple Tesla and video and microsoft google amazon and meta and again if those guys are all in the green uh you know with that set that's a positive contribution very in mind they are the majority of volume that we're seeing trade in the markets at the moment so you also use those again as another internal reference point and that's why i have them up in the screen here this watch list i have um it's basically my reference point when i open the charts in the morning i'm going to know first and foremost what the dollar's doing what yields are doing what the VIX is doing in the bond market then we look at the futures here and uh the overseas futures markets uh european bonds european markets major effects bitcoin gold crude uh the mag seven then uh below there as we move into into the cash session so again a bit of weight coming in here we're testing now 47 eighties want to see again watch the tick here we want to see some big tick prints if we're going to defend this area as as a reference we've got uh the value area low now has rotated slightly higher so we've got 47 76 as the as the value area low so if we start to trade down below there i think we could be starting to look for a um further downside price action 4770 then into the overnight lows 4763 4760 which would which would take out my my long position uh over and last night and so again if we move through there then my focus shifts to the downside and uh i'm going to be looking for downside targets and entries to or i'll be looking to add to my the short that i'm currently running from 4795 there's some uh we're starting to see some positive tick prints here develop five minutes got a nice response there and i see that one closed green strong green clothes want to see the delta flip bullish here as well if uh if we're going to defend this what you said yeah bummer index is picked back up training towards session highs 103 50s now again he's adding weight If the Doherb index more often than not is advancing, that's a risk-off indicator. VIX is picking up a little bit, 14-4 on the VIX. We were trading sub-14 at the open. So a couple of warning signs here for longs, but we are still holding in and around the full session with the full session VWAP. So again, there's nothing for me to do at this stage, and it's just the nature of the market. There isn't an opportunity, an immediate trading opportunity for me versus my strategy. So I'm just watching at this stage, I'm gathering information from other markets, using the internals to get a sense of where we may be headed. I have trade levels in mind, obviously that I've already given you pretty fine levels, where I'd looked to engage the market, but we are not testing those at the moment. And if you look at the overnight range, we're sitting right in the middle of it, and this isn't a high probability trade location as more often than not. We're just going to see chop here without any real strong rejection from that full session VWAP. When I talk about rejection, I'm talking about small impulse moves. So for me, a strong rejection from the test here into the full session VWAP would have looked for an immediate test, a pullback, and then to take out that IB high. And then that's that, if that momentum is building, and we're getting the confirmation from the internals, then obviously my focus is on the upside, and I'm looking for a breakthrough, the price cycle highs, the overnight highs, and then pullbacks to either buy on a pullback into predefined support, or first pullback, consolidate, and then play the break to the upside in the continuation trade, as long as we're getting confirmation from the internals and specifically the deltas. So if price is pushing through the high, I want deltas to be making new highs as a confirmation. And that's my trigger then to enter the trade to to join the trend. But at the moment, we are we're sitting pretty much slap bang in the middle. And there's nothing to do right now. The first 30 minutes of trade wrapping up here in a minute, if we're still sitting here in the midpoint of the overnight range, and not seeing anything meaningful developed, I'm not just going to stand here talking for the sake of talking. If there aren't any questions, then I'll allow you to join me in the Facebook group. And you can access, sorry, you can request access using using this link, facebook.com or size groups. Actually, I'll put that into the chat for those that are interested. And specifically, then you can you can access that. And then that will give you the link then to get through to the through to the Facebook, the messenger group, the trader chat. Thanks to the guys have posted the chat link into the chat on on YouTube there. Let's see where we are as we come into top of the hour. Destroyers are sitting in the midpoint of the initial balance. So we're holding 47 79 support and 47 90s resistance. So quite tight initial balance currently forming at 10 points. I've seen the AD line recover off the test of the zero line. All the breath remains neutral to negative. And the tick distribution, we haven't seen any ticks above the 500 level so far. So we're in there in terms of the tick. And currently we were seeing to try to pick up here as we as we hold the the VWAP and seeing more pressure here on the up tick. So as we try to get through the the current session mid. So the cash session mid there, 47 86, we're getting rejections. So we're still still not seeing any meaningful upside traction here. Value area low for the session has now we're testing it now at the moment. So we really want to see some demands that sort of bias start to step in here. If we're going to see this continuation move to the upside, I was still pushing higher along with the VIX game weighing on risk sentiment. Certainly bulls would not want to see the VIX turn positive on the day 29 2.6 4% but because of the level the VIX is trading at, that's kind of exaggerated. So I paid more attention really to that point 0.38. So we're not far from from flipping positive on the day in terms of the VIX at the dollar. Still trading above that 103 level reference that yesterday's technical trade setup video 103, 102, 50 area is going to be key. If we defend that, then I'm expecting the dollars to get another leg higher up into the 104, 104, 50s kind of video of that yesterday shared through the tip mill YouTube channel. Those that are interested, you can watch that yesterday's daily trade setups for what I'm anticipating. We'll see in the dollar, Tesla rolling over again, gone negative, holding, trying to see buyers are trying to defend the value area low. So you can see this green line is the value area low. This represents the base 70% of the volume traded is between 4790 and this 4780. And so buyers are trying to defend that area, build a base there to, we now have the volume pointed control for the session 4786. So that's the highest volume. That's when most of the price action has taken place since it was open up last night. So we're trading below there at the moment. So again, signals not giving any real clear reading at the moment. And we're stuck within a fairly tight initial balance for now. So I won't stay on here just for safety. We haven't really seen any significant move. Like I say, I'm currently short 4790 with a risk-free 4795 stock. I am long from yesterday to be 765 with a 4760 risk-free stock. I'm looking for potentially for my shorts up to get taken out. So if we take out the 4800, 4801, the range resistance, then I will be looking to play continuation trades to the upside. So I'm looking for a break, consolidation, then a break of the consolidation with the internals confirming. So I want to see positive AD line, positive breadth. And I want to see the deltas making new highs if I'm going to play the breakout as a confirmation. Alternative scenario is we take out the 64, the globex lows here. Then my attention is going to shift to the downside and I'll be watching for a break, consolidation and then looking to play continuation to the downside. My downside targets are the 4740, 4730 and the 4710 area, which are two standard deviation move. The 4832 is a two standard deviation move on the upside. Both that 4832 and 4740, I would look to play counter trend moves off, especially if we test those levels late in the day. But for now, I'm not too much going on. We have like I say OPEX, options expiration tomorrow. So that's likely pinning the price action in around this 4800 level for now. As always, traders, plan the trades. Trade the planner. Most importantly, manage your risk. I will run another live session next week, either Wednesday or Thursday. And I will update in terms of the confirmation of the day and access details into next week. Thanks very much. Hope you found this useful.


T. F. N. N. headline news update. Hi everyone, Basel Chapman, the host of the Tiger Technicians Hour, coming up straight after this T. F. N. N. Dune update. The Dow is up 52 at 26,771. Now the way I read it based on the Chapman Wave methodology, there should be a little bit higher highs this week to complete a pattern that says we should go to at least a leg C and then a leg D. We're at a potential peak B right now. In other words, four higher peaks from the low that was made at 24,701 on the 3rd of June and for subscribers to be still remaining long because we want to see this out to see if there's going to be a chance of a peak D in the in the daily chart. Now the S&P is a little bit different, but here comes the S&P. S&P is just a little bit different, but it has gone to an all-time high. The Dow has not gone to the 26,953 high, so the S&P also has slightly higher highs to come, I believe, and then we should have a bit of a timeout and the QQQ, which is the NDX100 is a little bit more advanced than the Chapman Wave methodology. It has gone to a potential peak C if there's no new recovery high today. And then I suspect we go a little high into the 190s. We're at 188.66. And if you look at the IWM, the IWM has been lagged for a while and lagged to gain today. It made that fourth highest peak at P&D. And so far this is the deepest pullback we've had since the beginning of the rally from the 3rd of June at 145.33. Now we're all interested to see what Gold is doing. Gold is up sharp. He's up 17 at a new recovery high at 14.17. This is a breakout pattern. And in that weekly chart, this is only a leg B. And it should actually go in a weekly chart to a leg D. It is about to test the monthly downtrend line. Look at this downtrend line that comes all the way back from way back in 2013. So there's a trend line that's about to be hit at exactly where we are right now. So if it goes to the 1422 level, that monthly chart is broken out. That's going to be important. And if you look at the dollar, the dollar's been pulling back very sharply. It's at 123. This is the fourth big red candle day. And it's just underneath trend line support. It's trading down 18% 96.03. Still, the longer term outlook is still looking good. But this is a big test of the day in the week here. I'll be back. We'll talk about it in more detail in my show coming up straight after this break in my Tiger technicians hour. And most of the hosts right now coming up. Hold on and we'll be back. Otherwise, I'll see you tomorrow.


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Hey guys, RealisticGame here. Today, we're gonna be playing Bad City and World Black. Oh god, what is going on here? It seems like there's a bit of mayhem going on over here. Did he just kill a cop? Dude, he's coming towards us!  Let's take this guy down. Oh, you're going down, buddy. There you go. We got him. Okay. Oh my god, but rest a piece of that cop. Alright, so you guys, I heard there was a serial killer on the loose summer in this Bad City game. But I'm not so sure. Let's go have a look around. It would happen to the guy. There was another guy here with me. I guess he killed him too. Oh, no. Okay, let's go down here. Let's get out. Wait, what is that? Dude, you guys see that guy? My god. Wait, should we just stay in the car? I don't think it's safe out here. Let's see what's up with this dude. Why is he in the road? Let's talk to him. Hello? Let's see if he replies. Oh my god, he looks scary. Kind of looks like Jeff the killer. Hello. Do you need a ride? Do you need a ride? Let's see if he wants a ride, man. He's stranded out here. Let's help this evil-licking guy out. Help? You need help? What do you need? What does he mean? You need help? What's up? Let's see what's up with this guy. What's up with this dude? Why is he just standing in the middle of nowhere in the middle of the road? I know what you did. What do you mean? He knows what I did. What is he talking about? What do you mean? What do you mean you did it? Okay, now he's like laughing. What? You killed her? What? Okay, he's saying I killed someone. Okay, I don't know if it's safe you guys. Oh god, he has a knife. No, let's get out of here. Oh god, I'm out of here, man. No, we're stuck. Dude, he's chasing us. Oh, do we have like boosts? Nitro, hit the nitro. Okay. Dude, I'm out of here, man. Oh god, okay, so this guy was just standing in the middle of the road doing nothing, licking at the ground. Something's not right with that guy. And then he says that we killed her. I don't know what he's talking about, man. I think he's just like a prisoner that escaped from the jail. It might be a little cuckoo in the head. Oh god. All right, but he said he needed some help. So I think we should go back and help him because he is out there by himself. Oh look, there's a flash coming. Oh my god, where did he go? Okay, so let's go see if that guy's still back there. Okay, so he was down the road. Oh look, there he is. How'd he get here so quick? Dude, he was all the way back there. Okay, he's licking at the ground again. What is he doing? Hey, mister. Hey, let's see if he replies. I'm sorry. He says he's sorry. For what, man? I was scared, okay? He was scared. What are you scared of? Of what? He said he's scared. Look out. Oh no. Hey, wait, she's punching the guy. Oh no. Wait, what's going on? Somebody's shooting. Oh no, he has a knife. Run! Oh no, he's stabbing me. I'm out of here, man. Oh god, they're shooting at him. Help me out! They just left him. They left me alone. Okay, so what do we do, man? I'm gonna take this guy. Hey, you need to relax, mister. Oh, oh god. And he's still running on the ground. Hey, man, you need to chill out. What's wrong with that guy? Why is he just staring at me? That's pretty creepy. I think we should arrest this guy. I'm sorry. What do you mean you're sorry? He keeps saying I'm sorry, but he keeps doing these mean things. It wasn't me. Okay, for sure this guy has to be crazy in the head. Then who was it then? I think he might have like different personalities or something. Why is he just running off? Because Anita chasing him. Okay, I can't chase her. Hey, what's up, officer? Oh god, she's punching him. So we just punched the guy. Come over here. Oh gosh. Let's just punch this guy. Let's all fight him. Now he's running, huh? The table's after him. I'm gonna take him. Hey, get out of the car. Now he's trying to run away. Come back here. Dude, he's quick. He's quick on his little feet, but Anita's quicker. Oh, he's trapped here. You trapped yourself. Oh god, he's running. No, he has a knife. Watch out. Oh gosh. Wait, is that a cop up there? Oh, that's a criminal. Oh god, I think that's his backup. Where is he at? He's throwing grenades. Oh my god. Wait, is it Anita? I let Anita deal with him. Actually, let's chase him. Let's see where he's going to try to run off to. Hey, that's my car, man. He just drove away my car. Who does he think he is? Look at him. He just ran over Anita. Wait, can we shoot him? Stop him, superhero. No, he's going. She went the opposite way. So much for a hero, huh? Wait, he just left with my car. Oh, he's back. Oh god, no. Dude, this guy's doing damage on me. Okay, so that guy came back with my car. That was nice of him. Let's go see what's up with them. Is that a... Okay, that's a hero. Bro, go get that girl up there. Oh god, now he's getting blasted by like some laser beams. That's what he gets for stealing my car. Hey, get out of my car, man. Get out of my car. Get out of my car. Oh, he's on my team. All right, he's a hero. What? The car just like crashed. Okay, hey, wait, can we lock him out of my car? I'm pretty sure we could. But I don't know how. What if I just found it? Camaro. Okay. Oh, I just found a different one. Okay, let's chase this guy. Where is he going? Oh, they got him. It seems like they ended his misery. Oh gosh. Okay, so I guess that guy's out of the picture then.  I want to test it out. Let's go be heroes. How do we switch teams? Switch to hero. Right, there you go. So I guess I'll be the fire one now. Looks sick. All right, let's go. How do you use this? Wait, I think that's a criminal trying to get into the superhero base. Let's go open the door for her, and then we'll just get her. She's not going to know what's coming for her. Let's open the door real quick. Oh, she's in the helicopter. The destroyer. Don't let her get in. No, she hasn't reached the premises. Get her. Don't let her. You shall not pass. Oh gosh. Oh, we got her while we were crouching. That was pretty cool, man. Nope. Okay, so we're here now. What's going on here, man? Okay, we got a cop here on site. Is that a bad guy? Nope, that's another cop. There's a lot of cops here, and they're not even stopping it. Well, maybe they're already dead, huh? Okay, let's go in here. Let's see if there's any robbers in here still. Oh, I got two of them here. You're going down, baking hair. That's right, you better not try to fight back because, you know, you're going to lose as long as he's running. He's in pursuit. Chase him. Oh gosh, he's dodging it. Oh no, the power of bacon. That is one dangerous bacon with an AK. Oh, you think you take me out, buddy? Oh no, there's two of them. No. Help me out also. Oh god. Okay, we got him. You're going down, buddy. Yes, we got him. Oh, he ranked up. Nice. Okay, so I think that was all the robbers. Okay, it was nice. We successfully stopped that robbery in progress. Okay, so now what? What else can you do in this game? Oh god. Okay, oh wait, can we? Oh my god, is that Jeff the killer? Is Jeff the killer again? Oh, but he's a good guy now, huh? It seems like he went from a bad guy to a good guy.  Last time I saw you, you were a criminal, man. I changed my ways. Oh my god, give him a round of applause. That's good for you, man.   All right, nice. Just, just what? Just what, man? Just I know. All right, good job, man.  You see, guys, he's changed his ways. You killed it. Okay, what does he mean? Okay, I think he's crazy now. He's trying to shoot me. Dude, okay, this guy's not right. Hey, I don't know, man. Okay, look at him go. Look at him go. Now he's running away into the distance. I don't know where he's going. Dude, is he running in the water? Is he going to run in the water? I think he's running in the water. Let's go check it out. Yo, what are you doing? You just can't swim out there. What are you doing, man? What's going on, mister? This world, what about this world? This world, that's what he's even, okay, what is he going to say? This world, that's not for me. What? He said the world, this world is not for him. Maybe he's a jailbreak kind of guy, you know? Oh my God. So you just swam away? Look at him go. And now if he goes into the sunset, even though there's no sun out, because it's nighttime. Well, that's the end of that guy, hopefully. All right, you guys, well, thank you guys for watching. Thank you guys for the amazing support. If you guys enjoyed the video, make sure to slap the like button. And this was Jeff the Killer in Mad City. And I'll see you guys next time. Bye.