Okay, so I have a question. Yes. Yeah. So where does overdamped I mean in the experiments you have shown like two of the experiments, the particles were overdamped, were they ever underdamped? I mean the dynamics was it ever underdamped? Yeah, in general it's underdamped because particles have mass, but it depends strongly on what is the sampling of the sampling time of the trajectory. So if you take snapshots of a particle in timescales at which they are larger than the relaxation time of the momentum, you can say that the momentum has relaxed and the only non-equilibrium variable is x. When you have this finite sampling, which is at delta t, which is larger than the moment of relaxation time, you can neglect the inertial term. And this is typically what happens in many experiments. So in many experiments, the relaxation time of the momentum is of the order of microseconds and one can sample the position of the particle in milliseconds. So you can neglect the inertial term in general. For the dynamics, for the thermodynamics one has to be careful and I can give you, okay, if you are in one thermal bath, you can use overdamped and there are no many risks, but when you have a space-dependent temperature you have to be very careful and I can send you some reference about it. But in the simplest case, isothermal system, you can use an overdamped approximation and get a good approximation for the heat. Okay. Okay, I can send you, please send me an email and I can send you some reference about it. Yes, sir. Thanks. Okay. All right. So if you have no other questions, I'll go on with the second lecture. So the second lecture is about stochastic entropy. So mainly what I like to discuss today is what I illustrate here in the second curve of our class is the second law in stochastic thermodynamics. Okay. So first of all, here is a reminder of what the second law says about macroscopic process. So you have here two snapshots and you know from intuition that this can be typical, this can be a process that can happen, a glass breaking into many pieces. However, this process doesn't happen spontaneously. This is very unlikely.  So is there a physical quantity that quantifies this fact? So this question has a positive answer. It's entropy production. What we say is that in the movie going from left to right, entropy production has increased. So the entropy of the system plus the universe has increased. Whereas when going from right to left, the entropy production has decreased. How can we see this? We can also see this in the compose the entropy production in two terms. One is the interaction of the system, which tells us, I call it delta assist here. This is related as you know, to the disorder. So typically systems physical process will lead to an increase in the disorder in the system. So here there is more disorder than at the beginning of the process. And also it will lead to dissipation of heat. Dissipation of heat has can be interpreted also as an increase in the disorder of the environment, which here I consider all the rest that is not this class. So typically we will see this type of processes. We will have increase in the environment entropy, increase in the system. But of course, think that here there is a law that says the law says that the total entropy always increases. So it is the sum of the system entropy and the environment entropy, which always grows or is equal to zero in equilibrium in microscopic systems. So this means that we can make a system more organized or ordered by reducing its entropy, delta system negative, but we will have to pay a price, which is increasing the environmental of the the entropy of the environment, which means dissipating heat. This is what classical thermodynamics says. Okay, so going back to classics here are two very important characters, Sallikarno and Rudolf Clausius. And they started the second law in the following way. So, okay, one thing is I highly recommend you to go through this book. If you want to refresh your knowledge about the second law is by Enrico Fermi. It's called thermodynamics. What do they say? So they say the following that imagine you do a physical process in which you expand the gas. You have a gas in contact with thermal bath. And what you do is you take this piston and expand the gas in this way. During this process, it takes place a dissipation of heat from the system to the environment. And I will call this Q. Okay. Now imagine you do the same process, expansion of a gas, but you move the gas infinitely slow. If you move it infinitely slowly, even if you do it so, so, so slow, there will be a dissipation of heat, which is called typically Q rep. It means the heat dissipation. Well, here I call Q to the heat absorbed. Okay, so Q will be negative here. So it's the heat absorbed when I do the process infinitely slow. The second law in few words safe for me. Any thermodynamic process dissipates more heat than when you do this process reversely. When you dissipate more, it means it is more negative. This is what this equation says. Okay. So in other words, okay, first of all, if something that was proved by Clausius is that the heat dissipated in a reversal process, it only only depends on the initial and the final configuration of the system. So it is a state function that is called entropy. Okay. It depends only on the final and initial state. And this is often, I will write it also like this, that is system. Okay. So this is a state function. And what the equation on the left is telling us is that is the following that the difference between the reversible heat and the heat is possible. And we can interpret the reversible heat, as I said, as the entropy change. And the heat divided by temperature is the change of the entropy in the environment. So we will assume the environment is necklid. So this means that this quantity here, delta s plus sn, which is the entropy change environment is always positive. And we can interpret this difference of this heat term divided by temperature as a sum of the entropy change in the system plus the entropy change in the environment. This is called entropy production s total. Okay. And this is always greater than zero. This is only zero when q is equal to q reverse or when you are infinitely slow in the process. All right. So this is the second law. It's written in stone as you see. Okay. This is true for microscopic process, very important. Excuse me. Yes. The difference between the up and down system was the speed of expanding the box. Yes. Yes. Yes. Exactly. This is slow. And this is faster. Any other speed. So this is infinitely slow. And this is at any speed that is finite. Okay. All right. Great. So what does this mean? This is also a reminder for isothermal process. If you do this process in a thermal bath, so there is a gas in a thermal bath of temperature t, we have that the entropy production is this formula, what we know. I just explained this. And now I will use this relation between the free energy, the energy, the system, is the system entropy, and this is the temperature. Just recall that when you have this type of relations, these, these, and these are system variables. This is not entropy production environment. These are system entropy. And this is from the environment. Okay. Just a reminder. So if you put this equation, if you put this equation in the first equation, you get this one. So I'm just replacing the definition of free energy. You get this. And now what I will do is I use the first law. So I write delta e as q plus w. And what I get is this equation. The entropy production is work minus free energy divided by the temperature. So this means that the second law, s dot positive means that the work done in any process is greater or equal than the free energy difference between the initial and the final step. Okay. Very, very simple. This is a classic example. Okay. What does it happen when we consider a non-isothermal process? So for example, if you have a gas, it is in contact with a thermal bath, hot bath during an expansion. And then we compress the gas when it's in contact with a cold bath. This is the working principle of heat engines, of the engine of a car, for example. And this leads to work because we are expanding the gas in contact with a hot bath. This is giving us a lot of energy. And then we are compressing when it's cold. So it takes us less amount of energy to compress it. At the end of the day, we get work out of this. So imagine I want to know what is the entropy production in a cycle. So after making a full cycle here. Okay. So in a cycle, delta f is zero because it's a state function. And then we just have q divided by t, but there are two baths, the hot bath. So the hot bath and the cold bath. Okay, q h divided by t h, q c divided by t c. This should be greater than or equal to zero. And if I now use the first law, remember in a cycle, delta u or delta e is zero. So the first law is zero equals, this is the heat plus the work. And the heat, of course, has heat from the hot bath plus heat from the cold bath. So I use this equation here. I get this condition, which is nothing else but the bound to the efficiency. This one here, this is the efficiency, is the work extracted divided by the heat intake from the hot bath. And this is a number that only depends on the temperature of the baths, not on the details of the system. So this means, I mean, in simple words, the efficiency of a Ferrari, of any engine, of any car is smaller or equal than the car efficiency. There is an upper bound for the efficiency of heat. Okay, this is just an introduction, but I will go through this more in one of my next lectures. Okay, another important key point from entry production is that it is related to irreversibility. So now consider a process at the finite velocity. So we have the expansion of a gas at the finite velocity. This is called the forward process, the one I'm showing here. And now say I will do the process backwards in time. So instead of going this way, I will go in the backward process, I will go this way. So I will go backwards. So if you do this and you do a snapshot of the process at intermediate times, like I show here in this red square, you will see that the system has differences. The distribution of the position of the particles of the gas is different in the forward and the backward process. So there is a degree of distinguishability of the arrow of time. So there is here, there is a relation between irreversibility and entry production. I say this because what one gets is that when you do a process infinitely slow, this is the reason that this snapshot that you take in the middle is not very distinguishable. But when you do this very, very fast, there is a lot of heat dissipation and there is it's much easier to distinguish forward and backward with a snapshot in the middle of the process. So there is intuitively a relation between heat and irreversibility or entry production and irreversibility. This is basic knowledge and this is what I'm trying now, I will try to explain also at the mescopic scale. So in classical thermodynamics, one cannot quantify irreversibility, but in stochastic thermodynamics, one can do it. And this is what my lecture will be about today. Okay, so now I enter more into the detail theory on this. I'll try to explain the second law in stochastic thermodynamics and mainly, I will follow this paper here by Udo Seifert in physical regulators 2005. This was a pioneering paper because it is where it was introduced, the notion of stochastic entropy and the second law in mescopic systems. Okay, so in this paper, what they discuss is, what he discussed, it's a simple system with a 1D over damped algebraic equation, like the one I was explaining to you yesterday. So we have x dot equals mu is the mobility. So mu, you can also say that is gamma to minus one, the inversion of the friction. And fxp is a force. And then this is the physical coefficient times, sorry, times y times. Okay, so one can describe this process in two ways. One is with this generating trajectories with non-jewan equation. And another one is in terms of the probability distribution, which is, for instance, you can use Fokker-Pank equation to describe what is the probability that, sorry, that the system is at x, at x at time t, sorry, sorry, at x at time t, given that it was at x0 at time c. Okay, this is what I would call pxp. We know from stochastic processes that for this equation here, the Fokker-Pank equation, the associated Fokker-Pank equation is this one. So we have partial t of txt equals, there is first a drift term, partial with respect to x of mu fp. This we can call it here the drift term. And then there is a diffusion term, which is the second one is d, the diffusion coefficient. And this is second derivative of txt with respect to x. This is the diffusion. Okay. Okay. And often we write this as minus partial derivative with respect to x of jxt, which this is called the probability current, probability current. Okay. This is standard in stochastic process. Okay. So first of all, one would like to define what is the entropy of the system. So in particular, okay, this is what I'm explaining here, in particular, I'd like to know what is the system entropy along a given trajectory, like the one I'm showing here. Okay. What is the entropy, system entropy along this trajectory? I expect that the system entropy will be also a stochastic process to do, for example, something like this. Okay. How can we define this? And here it comes the key definition in this, in this space. It is the following. So I do here a square system entropy at time t. We are saying what is the system entropy for a system that at time t, it's located in x. This, it's defined as follows. It's a definition that that's why I write here three equal nine is minus the Boltzmann constant times the logarithm of the probability to be at x at time t. Okay. Remember, kb, this is the Boltzmann constant. Why this is taking this way? Well, it is taking this way because when you take averages, so let's say you are at x at time t, but you would like to average this over many trajectories. So here I'm saying, okay, if I say x at time t will be at time t, I am here in x. Okay. But I'd like to know what happens when I average over many trajectories. So there will be, sorry, sorry, this is not correct. It should be here. So this is t and this is x. I'd like to know what is the average of this stochastic entropy along many trajectories. So there will be another trajectory that will be here. Okay, this time, it will be another x, it will be x prime. So if I take this object, system entropy, and I average over many of these trajectories at a given time, I get this, which is minus the Boltzmann constant, then I integrate over x with probability to be at x at time t. And what I integrate, what I average is minus kb log of p, which is what I'm putting in this integral. So you realize that here, okay, you realize that this one minus p log p is the Gibbs Shannon entropy. The Shannon entropy is defined as minus p log p integrated with dx. So this definition introduced by Seifert in this paper is consistent with the fact that when you average over many trajectories, you will get minus the Boltzmann constant times the difference in the Shannon. So it's related to the common knowledge of information that one gets. This is the uncertainty, h is often called also the uncertainty of random variable x. So this is the first key equation, which is the system entropy, stochastic system. As you see, if at time t, I am in x equal to 1, it's different that if I am at time t, I'm in x equal to c. So having said this, unlike now, to go forward, I compute how does this entropy change in time? So I have here the definition of system entropy, which is what I just introduced. And what I'll do now is to do the time derivative that I show here, time derivative of the system entropy at time. Okay. So now it comes a question that can be related to what I explained yesterday, how do we do time derivatives? So we can use Stratonovich calculus and do a time derivative as usual. So when you have a function of x and t, if you want to do the time derivative, you will have mainly partial derivative of A x t with respect to t dt. These are Stratonovich rules plus partial derivative of A x t with respect to x is Stratonovich dx. Okay. I'm sorry because I'm doing d dt. So what I have written is dA. So if you want to know d dt, sorry, d dt is just to go because I'm divided by dt. And this can say, okay, this is the way we take derivative Stratonovich. So we do this with this k v log p and we get, okay, the first term is partial s with respect to t, partial s with respect to t. So partial of log is one over p, partial p with respect to t. And the second is partial log p with respect to x. So it would be one over p, partial p with respect to x dx. Okay. Nothing else on that. Now I'd like to continue from here, which I will jump here. And to make this jump, I will just make use of the Fokker-Plak equation. So the Fokker-Plak equation I told you is partial t of p equals minus partial x of j. And j is, I'm just simplifying notation. This is the current mu of p minus v partial x of t. Okay. Of course, this f will be f x t. This is b x t. Okay. And then here is this b x t. But this is just to simplify it. Okay. Why I'm doing this? I'm doing this because I'd like to just change this by something which is related to currents and so on. So from this equation here, I can solve partial x p and it becomes just mu f, and I'm reading here, mu f b times p plus j divided by t. So again, well, mu divided by p is k v t. I'm using instant relations. So d is mu k v t here now. And then I have j divided by t. So I have changed this thing here, partial p with respect to x by f divided by k v t p minus j divided by t. So now I continue my calculation by replacing these two terms here. And what I get is the next line. The next line, well, I keep the same term here. And then for this, I put f p divided by k v t minus j divided by t. So I have first this one, f divided by k v t x d t. And the second one is with a minus j divided by d p x d. Right? This is what I get for the instantaneous change in the system entropy. And now I realize that the environment entropy, which I will write here in red, I said to you yesterday that this minus the heat divided by the temperature. And the heat is f dx. So this will be with a minus. This will be plus f dx d divided by k. This is from yesterday, from Secky-Mottoff. So I realize that here is what I put here, this term that appears in the derivative of the system entropy is minus the environment entropy. Okay. So I have seen that the system entropy, let me put it in the same color, system entropy. When I do this, I have, okay, there is a minus here and a minus here. So I have the environment entropy plus something else. And this something else will be the total entropy. This is what you can find here. The total entropy is system entropy plus the environment entropy. So if I take all this and I sum the environment entropy, they cancel and I just have this first term and the third term. So I get kb times current dp dx d t minus one over p partial t. This we interpret as the total entropy, the change of the total entropy between t and t plus dt. And you must recognize in this formula that it is fluctuating and it can be negative. So the change in the stochastic total entropy or the stochastic entropy production can be negative. Very important. It's can be negative. This is a key insight. So just I will take a different color. So for the total entropy, okay. And now you see we have environment entropy in terms of forces and displacement. System entropy is all this and the total entropy, it has currents, diffusion and problem. Okay. Another important point is that in the heat, you can measure the heat with one trajectory, but you cannot measure the entropy with one trajectory. Why is this? It's because we have here the object p. So the p is a wall that you always face when you work with entropy. So in order to know the entropy production of a trajectory, you first need to run the process many times and construct p and then know what is the p for your trajectory. Okay. This is a key difference with the first term. Okay. So let me go ahead. And now I will ask the key question is that do we have a second law? Because I told you this stochastic entropy can be negative. So then you should be awarded. So we claim that there will be a second law when we average over many trajectories. So let's now consider the average of this total entropy change over many trajectories. So if I go back, I just show you that we have this formula here. So I will take this and average over many, I will average with this probability pxt. So this is what I'm doing here. Excuse me, professor. Yes. Did you share with us these notes somewhere? Anywhere? I don't know on the side. Did you share them with us? Yes. But I honestly prefer that you take notes while you watch my lectures. I can share with you, but honestly, it would be much more useful for you if you try to follow me with your pen. Okay. Yes. But if the slides are already written, honestly, if I'm writing, I don't understand what I'm writing. Okay. Try to do your best. This is my recommendation, of course. But I'm happy to share the notes with you. Okay. Yes. If you can share, for example, these kind of notes, like if you write in the lectures and we can follow your pace, but if the notes are already written, I mean, there's no way one can write the notes and understand what's written in there at the same time. I think it depends strongly on the student. Yes. But after 20 years of university, this is what I found out, which is very hard to share. I'm happy to share. Especially when there's a lot of computations involved and one gets... Sure. Anyway, just remember that... The various calculations. Yes. I fully agree with you. I will share my notes, but just be aware that this will be also in YouTube. So you can also follow this. I will share the notes with you anyway. But please just follow my lecture live and I'll pass you later the notes. Okay. Thank you. Very good. All right. So let me continue. So then what I will do now is to take the average of this object. So I have a first term that is the average of partial tp with respect to p and a second term, which is the average with respect to all the characteristics of this term that contains the fact. First of all, the first term is equal to zero, the average. And this you can see it easily in the next line because when we do this average, sorry, when we do this average, this means average with respect to the process. So it means we will average with p. We have to put pxt to average with px. So it turns out there is a p in the bottom and in the numerator, so they cancel. So we just have partial with respect to t of px dx. And this one, so you can take the time derivative out and this is equal to one, so the derivative of one is zero. The first term is zero. Be careful because this is fluctuating, but all average is equal to zero. So now I come to the second term and the second term is as follows. So we have j divided by dp dx. Then I will take the dt below later. And by now I don't take it. And now what I do is I use the Langevin equation. So remember that I have it here dx dx equals mu f dt plus square root of 2d dv. So I plug in this here and I have the first term, which is with mu f dt and the second term, which is with dv. Remember, I'm doing everything in Stato Novics. That's why I have this circle here. But for the sake of calculations, things are easier to calculate in Ito. So I use again the same theorem I called yesterday. And what I get is, so I transform this one in Ito plus the term with dt, which give me a second. No, sorry, sorry. I am here. So I will have with dot dx. Then I will have a dt term. And I will have a second dt term here. So this comes actually from this one. Both will contain a dt term. And on top of that, on top of that there is a, sorry, sorry, sorry. I think I made a mistake. Give me a second. This is dx. This is correct. Then there is a dt term. This is partial x of j. Okay. And then there is j p square. Okay. Okay. Give me a second because I don't see it now. Okay. I will have to check this later. But if you apply this rule to this equation, you finally get, okay, the first term is here. So it's mu f with Ito. Now we have this one in Ito as well, which is square root of 2 dv in Ito. And then finally there is a dt term that comes in this way. It's j partial xp where the p square dt. Okay. This comes from transforming this into Ito. All right. So after all, one thing you can see is that after all this calculation, s dot total becomes here. So you have j divided by, sorry, j divided by dp. Then you have mu f. And then you have a term which is partial x of p. So if you go back to the focal point equation, you can check that the total entropy becomes, this is just a mathematical manipulation. It becomes j divided by dp square mu f minus d partial x of p. Okay. This is the key result. So you will have a term here, multiplying by another term that turns out to be also j xt. Okay. We come back to our definition of the focal point equation. This is the current. So we can say this is j xt. Okay. Just mu fp minus d partial x of p, right? So when we average over many trajectories, we get that the total entropy and over many trajectories equals kb j square divided by dp square. So it turns out that, okay, this is j to square. So this is a positive number. p square is also a positive number. And this is the diffusion coefficient, which is a positive number. So we get that the entropy production on average is greater than zero. This is the way we formulate, sorry, the second of thermodynamics. So it holds on average when averaging over many trajectories. Okay. In other words, one can also take from here and take the average in this way. So remember when I do an average, it means that I, okay, any average here, it means that I am doing an integral over px of pxt. Any average or something that depends on time. Okay. So when I have this average here, what I have to do is take this, multiply by pxt dx and integrate. So when you multiply by p, the p square denominator becomes p, like here. And then you have this. So it turns out this is the analytical expression for the average integral production in an algebraic system. And this equation reveals one thing. It reveals that it is zero in equilibrium because it depends on the current in ij square. And in equilibrium, there are no currents. Okay. So for instance, if you have a two-state model, which will be of state one and state two, and this is a very little balance. So you have no current between state one and two, no net current. Then the integral production in this model will be zero. However, if you have a system, which has three states, for example here, one, two, three, and the rates are not balanced. So for example, there is a higher rate to go this way than to go backwards. This rate is smaller and then the same here and the same here. And then here we have a smaller rate, like this. In this case, one has currents. So if you look at the current between two and three, the current, the net current is going this way. So we have a clockwise current in this system. In this system, J will be different to C. So then we will have entry products. So this also relates to the idea that we had before on relating entry products with irreversibility. As long as you have a system that goes more in one direction than in another, you will have positive current and this will lead to entry products. Okay. So an important insight that I really want to highlight in this lecture is that the total entropy along a single trajectory is this formula. So we calculated the change. This is what we calculated up to here. This is d s dot pt, or ds in this case, time. If we want to know the entropy up to time t, we have to integrate, okay, this is equal to the integral of basically delta s dot s from s equals 0 to t. And this is nothing but the integral between 0 and t of s. Okay. It's just, sorry, this one. Okay. So as we know, we have calculated it and it turns out that you get, sorry, we saw it before. So we got this from before. So we got it actually here, this formula. This formula is stochastic entropy along a single trajectory between t and t plus dt. So if we integrate over time, we get this one. And what is very important is that this formula can give any number. It can be very negative, very positive, and so on. The only thing we are ensuring right now with this formulation is that it's average at any time it's always positive. Okay. This is the way we formulate the second law in stochastic thermodynamics. All right. So we can also do this up to now. I've done this for continuous systems like Klein-Jobin, but we can also extend this to discrete systems.  We have discrete states, a thermal bath, and a system that jumps between these states. Of course, in general, one has rates that are independent like this. But the simplest case and situation is when these rates are time-independent and we can look at either equilibrium or non-equilibrium steady states. So when you have equilibrium, typically, you have this relation, which is relating the rate in going from state m to state n to the rate in going in the opposite direction from state n to state m. In equilibrium, these rates obey this is the condition of detail balance, which implies that the net current between any two states equals to zero. You can check yourself that the equilibrium probability times, so this would be the net current per unit of time between state m and n. And this would be the net current between state m and n and this is n to m. So if you plug in the Boltzmann distributions here, you will see using this condition that you have no current between any two states. However, when you are out of equilibrium, you break this condition. Out of equilibrium, you don't have this relation and you have something that is a generalized detail balance condition, which we call local detail balance, detail balance. Sorry, let me have some trouble to write with this balance. This is the condition of local detail balance in which we relate the rate to go from n to n to the rate to go from n to n with the heat dissipated in the transition. Here, we don't have the energy that we have only the heat and this is a crucial assumption that we take in stochastic thermodynamics. In other words, we say that the transitions are triggered by the environment. So when you have minus q divided by t, this is the same as saying the environment entropy divided by q. So this is a assumption that we do in stochastic thermodynamics and actually we define the environment entropy like this and it will be crucial later to define entry products. So let me now explain briefly how do we calculate the entry production from state x to state x prime in a model like the one I just showed before in other sketches. So in order to compute this, we will say, first of all, we have the same definitions as in the case, sorry. In the previous slide, can you explain again why this local detail balance, why is it s environment? So this is an assumption that we do but it makes a lot of sense in many physical systems. So for example, when you have, for instance, okay, harmonic potential, you have a particle and you will say, okay, how can I jump between this state and this state? Okay, so this jump is, sorry, is often triggered by, this is not coming, the energy that the particle is taking is not coming from an external agent but it's coming from the, from the bath. So what we say is that when the particle is jumping between a low energy state to a high energy state, it is because it has absorbed a certain amount of heat from the bath. Now we say if we are here and we jump backwards, so we are doing the same transition, we will dissipate the same amount of heat but with a minus sign. This is a very, let's say, standard assumption in stochastic thermodynamics. In order to have this type of dynamics, this type of dynamics implies this condition here. Okay, I'm just trying to explain this in a very, very simple language without giving you too much math but this condition reflects the fact that when you have a jump, one state to another and a jump between the reverse jump, you dissipate an amount of heat that is minus the heat that you absorb when you jump between state A and state K. So it's just a consistency, consistency relation for this type of systems. Sir, then shouldn't it be two times of this or I mean, I'm just saying something wrong. Why two times? Because like forward jump, the rate of forward jump is proportional to e to the power minus q and then rate of backward jump is proportional to e to the power q. You have to be a bit careful with this. The rate of jump backwards is not always proportional to e to the minus q. What you know from, okay, this is a random formula like this but when you have this type of dynamics like the one I show here, this is not always and you can show this in many physical models. You don't have always that this rate is proportional to e to the minus q. It is not. Be careful with that. Which makes more sense is this condition, okay? Excuse me. Yes. But aren't we neglecting the possible presence of work, external work? Yes, but okay, when we deal with discrete systems is what I discussed yesterday. Okay, one assumption that we do is the following. When we have two levels or two states, let me call state zero, state one. When we have two states and a system that jumps between state zero, state one, we say that the energy change in this transition is all heat. Okay, so here let's say for example this is cavity. Here the energy change is cavity, right? And we are saying that this equals to q plus w but in our definition of stochastic thermodynamics, we say, sorry, I lost it. So give me a second. Okay, I lost all my, okay. So we say that when you have a jump between zero and one, there's a difference of energy which is delta e equals cavity. And we take this as, well, this is an example when you have a barrier of other cavity. This is an example. Okay, here we say that this is all heat. Whereas when you have a system in which there is no jump, but we raise a barrier to up to cavity, for example, we take this energy change as work. Okay. Okay, thank you very much. This is because of the definitions we are using. Okay. All right. And does it make sense now? All right. So we are assuming this that jumps between different states are triggered by the environment and therefore they dissipate heat and changes in the energy in which the system is not jumping to different states are due to external agent. This is our assumptions. That's why, that's why here we just say, right. So this is a crucial assumption and you will see why this is so crucial in the next slide. So in a discrete system, we have a jump between X to X prime. We can still define the system entropy as we did before. And the change of the system entropy in this jump will be the system entropy at the end, which will be minus kB log P X prime minus the system entropy at the beginning, which is minus minus, which is plus kB log P X. So you can also write it like this. Okay. Minus kB log P X prime P is the probability to be in state X prime. So you can write it like this. On the other side, the environment entropy change, you can write it as kB times the logarithm of the base of it in the rate to go from X to X prime and the rate to go from X prime to X. So why this is nice? It's because when you sum this plus this, you get, this will be the total entropy change time t. You get that this is equal to kB times logarithm of probability rate probability rate. So mainly, this is nothing but the probability, the joint probability to go from X to X prime. And this is the joint probability to go from X prime to X. So, and this is the formula that I'm trying to illustrate here. The total entropy change between t and t plus dt can be written in terms of joint distributions. This is the both one constant times the logarithm of the probability to see at time t, the state X, and at time t plus dt, the state X prime divided by the probability of the reverse trajectory. This is at time t, the state X prime, and at time t plus dt, the state X. So in a different way, we can also do it, I mean, this is a sketch. This is the probability of the logarithm, this is the logarithm of the probability to see first a circle, then a square, or first a square, and then a second. So this is the time reverse trajectory. The nice thing of this formulation is that you can really see a relation between, you can see it like this, a relation between entropy production and irreversibility, because this is related to probabilities of trajectories and time reversals. We will see this later in more detail. Okay, so something that is very important is that the environment entropy change is seen on outside jumps. So as I said, when we have a jump, so we have a jump between one state to another, we say there was environment entropy change. But when you are in one state, and you change the energy of the state, there is no environmental change, it's just work. So very important, outside jumps, the environment entropy is the changing environment. Okay, another thing is the system entropy is typically on average zero, because it's partial zero P, and we showed before this is on average zero. And the total entropy production, which I defined before, you can also take it, sorry, take it and sum this over all the trajectories, and what you get is this formula here, the total entropy production has the system entropy change, and the environment entropy change, which is the sum of all the jumps, so it's the sum of all this here, this is in one jump, from x to x prime, but in a trajectory, we have a lot of jumps. Okay. So if we want to know the environment entropy up to this time, we need to check the environment entropy in this jump, then the environment entropy change in this jump, environment entropy change in this one, and then in this one. Okay. That's why the total environment entropy change is the sum over all the jumps of the logarithm of these transistors, okay, the rates of the transistors. A nice thing is that later on you can also take averages of these quantities, so it's very similar to what I showed for the Langeman system, but now we have to sum over all possible states, and you can also write it in terms of the currents, this is, you can show very easily, and you can do this with the total and the environment entropy and system entropy, so these are analogous formulas to what I showed for the Langeman case. And I will come now to a very crucial formula, which is what I was trying to explain now, is the relation between stochastic entropy production and time irreversibility. This is what I'm going to show now, it's very general, so here I showed for discrete systems, but you can extend it to continuous in this way. So the way we do this is as follows, we define one object that is px, well, sometimes I use this notation, and sometimes I will also use tx, tbar to denote a trajectory, this is the path variety density to observe a trajectory in the forward protocol, so we have a forward protocol, and we look at what is the likelihood to see a given trajectory. And then we look at another distribution, which is p tilde of x tilde, it is the probability to observe the time reverse trajectory x tilde in the time reverse protocol lambda tilde. So let me give you an example, one example is what I show here, so we have a process in which we go forward in time like this, so we are changing a control parameter from value lambda x to lambda b, and this produces a given trajectory like this one I'm showing here. So this first object will be the probability to see this blue trajectory in this process, which will be this black line is grown, this will be the process running in time like this. The second object is the probability to see the time reverse trajectory of this one, which will be a trajectory doing like this, in the backward process, the backward process is running in the other direction, so now the backward process in reality is running like this. Okay, so now the black line is being done from here to here. As you see, this won't be this trajectory that I'm showing, when I show it in blue, it's a typical trajectory for the forward process, but it's a very atypical trajectory in the backward process. So one typical trajectory in the backward process will be like this. Okay, this happens far from equilibrium. When we do this process very slowly in equilibrium, this means that the system can follow the protocol in equilibrium, then it will be, we won't have this type of hysteresis in the arrow of time. The system will be, all trajectories will be equally likely forward and backward. We also have to add an assumption and check later mathematically, which is this one, and then this leads us to show that the ratio between these probabilities, path probabilities, you can write it as follows as, okay, this is the ratio between the initial and the final state, and then we can, okay, we can factorize this path probability as initial state and then probability of the rest of the trajectory given an initial state. And this one, you can break it in the same way I was breaking it now in terms of, I was breaking it before in terms of environmental entropy, you can write all this as e to the minus beta q. This is an essential, an assumption is to classic thermodynamics. This object equals to e to the minus beta q, and this is the q associated to this project. Okay, what about this? So this, you can write it as e to the minus log of the ratio of this, and this is the system entry. So in the end, you get the ratio between two, so probability of the trajectory forward, probability of the backward trajectory, the backward, you write it as exponential of the total entropy associated to the entire trajectory, this one. Okay, this is a very important formula, and here I show a simplified notation you can find in many papers and books, which is this one, px divided by px reverse, so p reverse, the important p reverse of px reverse equals e to the s dot of x of the trajectory divided by q. And this is a central result is to classic thermodynamics, that the total entropy, so I'm taking logarithms in left and right, in the reproduction associated to a single trajectory, I write here as s dot, but in reality this is s dot evaluated at x c dot t is Boltzmann constant times the logarithm of the probability to see the trajectory divided by the probability in the backward process to see the time reversal. Well, what does this mean? This means that in equilibrium, all trajectories on the time reversals are the same, so this object stochastic entropy is equal to zero at all times, so if it goes, in this figure I show here, it goes always in zero, in equilibrium. In non-equilibrium, that probabilities and the time reversals are generally different, so the enterprise of fluctuates can take any value as long as its average is positive, and this is what I show here in this trajectory. Okay, this is the entropy production along any non-equilibrium process. It can even take negative values, okay, this is very important. This is a central result in stochastic thermodynamics, and I can give you a simple example, so things are not so abstract, and a very simple example is here, so we have a particle in a, I think it should be close to finish, but let me just finish with this example, just one minute. We have a particle in a linear potential, a particle, of course, has a tendency to go more in this direction than in this one, and if you compute entropy production for this example, this flangevan equation, you can show it takes this simple expression, so it's just proportional to the position of the particle, so it means that when you go down, you go with the, with the net force, you produce entropy from this formula, entropy is positive, and when you go up, entropy is being reduced, total entropy production, stochastic entropy production is being reduced, so these events can happen because there's a system with fluctuations, and this is quantified as a transient negative entropy in the dynamics, okay, negative stochastic. All right, so I will stop here, I had more to say, but I think we can, I can explain this in the next lecture, and so I prefer to leave room for questions, if you want. Any question? Sir, like in the, we found, I mean, in that paper, is it just the average value, or does it comment about the distribution of total entropy? In which paper, sorry? In the site itself, I mean, the one which you're trying to describe. Yes, this paper, well, they discuss the fact that it can't take any value, this is discussed there, but distributions are not provided in this paper, it is a very theoretical paper, almost in the same way I explained, okay. However, you can find distributions in other papers, like for example, I have one example, right, this is a, okay, this is one example, these are physical regulators, which came after, right after that paper, and you can find in this paper, they do a quantification of stochastic entropy in an experiment, and they plot distributions, and the distributions you can find negative values, so that I can give you more reference if you are interested. And like one, maybe basic question, why is stochastic, I mean, entropy production of like very, I mean, people are interested in it? Okay, this is a very, very big question, I must say, but people are interested because it's a central quantity in thermodynamics, you can see it right in my second, you can see it, trying to go back to my presentation, you can see it already here in the beginning of my lecture, entropy production implies bounds and constraints of physical processes. It's one of the most universal laws, the second law. So for instance, if you apply the second law to an isothermal system, you see it implies a constraint on the amount of work you can extract from a physical process. If you apply it to a non-isothermal system, it implies a bound on the efficiency of a heat engine. If you apply to any other system, it will imply constraints on the energetics of different systems. So it is a universal law that has very relevant implications on different physical processes, but people are interested because of its universality. It's probably the most universal well-known principle in physics, the second of thermodynamics. Yeah, I agree with that, but as you have shown us now, this is not really as universal in the sense that the average is not really greater than zero. I mean, only average is greater than zero, not the total entropy. So I mean, is it like I was thinking something experimental, you're saying something on the universality lines? Yes, so this would be something I will discuss in the next lecture, which is about fluctuation theorems. So in the fluctuation theorems, this was a key discovery in the field, and it was found that there are also universal laws for the distribution of entropy production. So the distribution cannot be arbitrary. So there are constraints on you cannot be at minus infinity for free. So there are constraints on what is the probability to get very negative entropy. This is something that is very new, while it's new in the last 30 years, and it has been found in what is called fluctuation theorems. So I think your question is very important, but I will give you an answer hopefully in the next lecture, because if we discuss exactly this, why are we looking at negative entropy and what new results appear for this negative entropy in this field? Okay, and just one last question. How does this system entropy generated in, I mean, sorry, entropy of system is given by Q reversible by T for a simple process. How does it sit with stochastic thermodynamics? I mean, can we actually see that it's similar in average sense? Yes, you're also advancing something you wanted to say yesterday. So of course, if you use this definition that I'm showing, it's something totally statistical. So this is probability for a trajectory. You don't need to have physics here, right? You can take a financial system and compute the probability of a stock market to have a certain value, right? But the key point is that you can now compute this quantity, this p over p reverse, and go to an experiment and find that this is related to the real heat in the device. And this, for example, okay, I didn't have much more time, but it's good you make me this question. We did this in a paper. This is 2019 and we published this with an experimental collaboration. This is an electronic system which has four states and you can compute this statistical quantity log p over p reverse of trajectories because it's a Markovian process. And you see here on the right experimental time traces of the stochastic entropy. And the slope of these curves is s dot dot, which I was explaining today, is related to the joule heating. So you get that this dot is minus the heat of the temperature and the heat in this system is an electronic system. This is the joule heating is the intensity of the electrical current times the voltage. This is a system that has a DC voltage applied. So it seems it's very statistical, very esoteric, but at the end of the day, this slope is related and this stochastic entropy on average is related to heat in many examples. Okay. Okay. Thank you. Okay. Thank you very much, Edgar. I think we need five minutes of break and I'll stop recording.


Your Coca-Cola bottler presents, Claudia, based on the famous play and novels by Rose Frankin. Brought to you transcribed Monday through Friday by your friendly neighbor who bottles Coca-Cola. Relax and while you're listening, refresh yourself. Have a Coke, and now, Claudia. Momma, you asleep yet? I'm glad you're not.  I'm on the bed. Don't mind my way. I came to borrow something from you. That's what you keep a mother around for, to borrow things from her. Well, aren't you glad you're good for something? Small pittance.  Do you have an old pair of white cotton gloves? White cotton gloves? Yeah. Didn't you just say you were on your way to bed? Yes. Now you want to borrow a pair of white cotton gloves? Mm-hmm. Didn't that wait for tomorrow morning? Well, I want them tonight. Let me get this straight.  Exactly. Is your headache very badly? Momma, for heaven's sakes, what's so strange about wanting to borrow a measly pair of white cotton gloves? I don't want your good ones. I want your oldest worst ones. I'll ask no questions. I don't even want to know the reason. I probably wouldn't believe it if I was told. It's very simple. No, no, don't tell me now. What drawer do I keep? Oh, yes. Yes, this one. Momma, be sure to give me your oldest pair. No, don't worry. I have no intention of giving you my best for whatever it is you wanted. I don't know what you're thinking, Mrs. Brown, but I just want these white gloves to wear. I didn't expect you to hang them around your neck. They are for my hands. Oh, I thought we were wearing white gloves on our feet this season. If you'd listen, they are to keep my skin nice and smooth when I go to bed. Of course. Then when you get up, it doesn't matter what happens to them.  Here's a nice old pair. How are these? Perfect. They have two holes in them. Thanks, Momma. Don't thank me. Just leave me alone so I can get my beauty sleep. Sleep late. Don't bother about waking up for breakfast. I don't need that much beauty sleep. Thank you. I take it. You meant that as an insult. Of course I did. So long, Momma. Close the door well, or it'll rattle all night. Doors in houses that David builds don't rattle. Remember that. I'm back, David. You're not in bed yet. I will be in a jiffy. Momma, sleep. Heavens, no. You think I'd wake her up? I think you would. I haven't brushed my teeth yet, so don't hog the sink. I never hog anything. Oh, it's a beautiful night, isn't it? It's so clear and cold. It's going to be wonderful sleeping up here in the winter, isn't it? Have you ever had any trouble sleeping? No, but I just expect you to enjoy it more up here. Say, David, how do I look to you? Same as usual. Am I wearing well, would you think? Wearing well? Wearing what? Am I well-preserved for my age? I'd say you look just about as old as you are, and you act at least ten years younger than you are. You sure I don't look any older than I am? Hard to tell. I'm so used to you.  You're not bad-looking. Nothing sensational about you. I don't suppose I'd turn around on the street if you walked by me, but you were pleasant to have around. Don't knock yourself out giving me compliments. I won't. Sometimes I wish I... Stop wishing anything, darling. I married you because you're you.  Me doesn't sound very exciting. Why couldn't I have been born with lavender eyes and auburn hair?   My brain's all right. I have you. And what do you want with lavender eyes and auburn hair? You have me without them, too. Aren't you satisfied? You don't understand. I'd love it if you thought I was the most beautiful woman in the whole world. Maybe you are. To me. Am I? Hey, what brought all of this on anyway? Oh, nothing. Except you're so handsome in your pajamas. You look pretty nifty in yours, too. That's a good doodle. I want to brush my teeth. It's a lucky thing I don't have an inferiority complex as big as a watermelon. I don't know what gets into women. You meet them, you court them, you propose to them, you marry them, and then for no reason they want you to tell them that they're beautiful. Hey, where are you? I'm in the bathroom. You think you'll want an extra blanket tonight? Dip your finger out the window, see what it's like. I did. It's cold. Why are you bothering me about the extra blanket? Because you're the boss of the household. Since when? Since I promoted you from boss junior grade. Now, what have I done to deserve that? Oh, I'm a very generous guy. Hey, Claudia, if I haven't say carry off, I want to get to bed before the sun rises. All right. You can go in now. Oh, thanks, great. Claudia. What's the matter? Your face. What have you done with it? My face, David? Well, I haven't done anything with it. It looks like patent leather. Oh, such a fuss. I just put a little nourishing cream on it. Nourishing cream? What for? For my face. You look terrible.  It's a means to an end. I can't take it off. What's the end? No wrinkles, beautiful skin. There's nothing a matter with your skin. Not yet, maybe, but Julia said that I... Oh, now you're listening to my sister-in-law. Well, she knows more about these things than you do, or I do. That's all she knows about. Now, that's not true, and you know it, David. You said yourself she has a wonderful brain for stocks. Well, what did my esteemed sister-in-law say? Nothing, except if I don't want to get wrinkles or dry skin, I should take care of myself now. Also, I have freckles. You have three. Four. No, and I know that. Four. Four on the bridge of your nose, and I like them. You're not supposed to. I don't care if I'm not supposed to. I like them. You leave them right there. I married you for those four freckles. At last I know the reason. Well, anyway, what's so terrible about me putting a little nourishing cream on my face? It's not a crime. It's just that it's not you. That's good. Why can't women leave themselves alone? The minute a woman gets a man, she starts trying to change herself, improving herself. Doesn't she realize that her husband married her because of the way she was? Well, I'm just trying to keep myself the way I was. I'm getting older. If I don't take care of myself, I'll look a mess when I talk. When you're 20. Well, I don't see why you're making such a fuss about me putting a little nourishing cream on my face. It looks so sticky. It'll get all over the pillowcases. I'll put a towel on the pillowcases. Then it'll get all over the towel. Well, that's what the towel is for. Now, where are my gloves? Your gloves. Certainly, I want to put them on. That's what I borrowed them from Mama for. Put them on so the cream will stay on my hands all night. Your hands, too? Oh, they're the first things that show age. Julia said. Julia knows. She pays a fortune to find these things out. I'm not too proud to learn secondhand. Well, all I can say is, you look pretty ridiculous going to bed with your gloves on. Oh, wait till you see my hands in the morning. You'll sing another tune. You look so greasy. It washes off. I doubt it. Oh, you're so sweet. You make me feel so good, darling. David, this is the best nourishing cream on the market. Quite expensive. It'll do wonders. The wonder is that you're willing to buy anything expensive. Oh, I didn't buy it. No, I got it free. I bought cleansing cream, and they gave me this little tube as a sample. Oh. Someday I'll use the cleansing cream, too. When I need to be cleansed. The workings inside of your head are really unique. They should be written up in a medical journal. There, I feel all wonderful and sticky. I bet you Julia notices the difference the next time she sees me, even if you don't. I notice the difference already. You do? Bad. Thanks. Hey, I thought you were in such a hurry to brush your teeth. I was. That's what I'm doing. I must admit you paralyzed me, all nourished up with cream. Shall I put out the light when I'm through? Put it out. I'm practically in bed now. David, what's the matter? Oh, David, I can't understand a word you're saying. What's the matter?  I can't talk. David, you're sick, darling. What happened? I thought you spoke a lot of... Try and talk quietly. I can't understand you. What's happening in here? I thought I heard someone shouting. It's David, Mom. I don't know what's gotten into him. I'm going to tell him to look. He's watching the trouble. He's in the bathroom, Mom. He's just brushing his teeth and always getting to bed. And all of a sudden I... Well... Well, look at him. David, calm down. What is he? Calm down. He's foaming at the mouth. David, you're drooling on the carpet, darling. Mom, is he having a stroke? Now, David, just tell us. What is it? What happened? Nourish cream. Oh, darling, I can't understand a word you're saying.  He has a wild look. No, no, no. What is it, David? No, no, no, no. Not cement. Say it again slowly. I'm saying it. Not nourishing... Nourishing cream, not cement. What? He says nourishing cream. Is that what you said, David? Just nods. He's nodding, Claudia. Nourishing cream? It's on my face, David. On my toothbrush. On your toothbrush. I thought it was toothpaste. Mama, he says he thought it was toothpaste. Oh, is that all?  It's all sticky. I can't talk. I feel like the back of an envelope. Mama, should we help him? Well, I don't know what we can do. How does one take nourishing cream off? I don't know. I just put it on. I suppose he ought to wash his mouth out. Well, if somebody do something, I'm going to be sick. Let me see. Washing doesn't take off creams and oils, does it? No, water and oil doesn't mix. No? Then what do you think you ought to do, Mama? No, this is awful. How will I get you for this? I know, Mama. Soap. That's right, Claudia. Soap.  Nice, strong soap. I'll go down and get the kitchen soap. If you move, if you move, I'll... Oh, this is the worst stuff I ever did. David, don't just stand there. Do something, dear. I'm going to do something.  You're going to take me over your knee? What have I done? You left the top off that tube. You left it right next to my toothbrush. You had to go out and buy it in the first place. If you don't look before your brush, that's not my fault, David Norton. Besides, I'm the one who should take you over my knee. I'm busy. It's so sticky. Just because the cream says nourishing cream is no reason why you should eat it. Try and swallow it, David. It's mainly vegetable. Swallow it. No, no, no. Not that. If you weren't so pathetic-looking, I'd be furious with you. My nourishing cream, the most expensive cream on the market. You had to go wasting it, eating it, brushing your teeth with it. Are you scolding me? David, don't look at me like that. That was the end. Hand me the hairbrush, Mother. Don't blame your David. Here's the brush. David, what are you going to do? Lean over, young woman. David, don't do that! Hey!  The pleasant custom of pausing to hear a favorite radio show in the midst of the day's work can be made even pleasanter. If you get a bottle of Coca-Cola from the refrigerator before the program begins, delicious ice-cold coke is always welcome. And even the best of entertainment is more appealing when you listen refreshed. Oh, Mr. King. Yes, Mrs. Brown. Tell me, how can David get rid of the flavor of nourishing cream on his palate? Let me see. How about a little kerosene, maybe? An excellent suggestion. I'll tell him. Just don't say I suggested it. He's scrubbing away this very moment with soap and toothpaste. Oh, I feel for David.  Well, I guess I better let you get back to what you were going to say. We'd all planned to get to bed very early tonight, and here it is late again. Yes, that's right. David's going back to work Monday, isn't he? Yes, the first day since his accident. Quite an event. Indeed it is. Congratulations for me. I will. Goodbye, Joe. So long, Mrs. Brown. As I was about to say, every day Monday through Friday, Claudia comes to you transcribed with the best wishes of your friendly neighbor who bottles Coca-Cola. So listen again Monday at the same time. And now this is Joe King saying au revoir. And remember, whoever you are, whatever you do, wherever you may be, when you think of refreshment, think of Coca-Cola. For Coca-Cola makes any pause the pause that refreshes, and ice-cold Coca-Cola is everywhere. The parts of Claudia and David on this program were played by Catherine Bard and Paul Crabtree, and the entire production is supervised and directed by William Brown Maloney. And now here's a word from your friendly neighbor who bottles Coca-Cola.


Four things narcissists do when you're not there It may often seem as though the narcissist wants to be alone But narcissists hate being alone They cannot live without supply They cannot live without attention from other people They need someone to impress They need someone to deceive So that they can fulfill their wants and needs And at one point you were that person Until the narcissist got bored Until they began to lose interest in you until they took you for granted and That's when they decided to have something new They wanted that buzz they get from meeting a new person Which is why they didn't mind neglecting you They didn't mind tossing you to the side Because they needed more time to focus on other things That is when they will say they need space They will end your relationship suddenly and without explanation They will withdraw from all communication Or they will become very offensive and bad manner towards you They will push you away They will start arguments with you for no reason They will blame you for everything Until you feel like your only option is to give them space But they're not revealing their true intentions to you They're not telling you the real reason why they want space Because they don't want you to know what they're up to They want to keep you in the dark Which is why I decided to create this video To shed some light on what the narcissist is doing when you're not there One, they are seeking new supply The most obvious thing the narcissist does When you're not there is they seek supply They're trying to impress a new person Because they prefer to have multiple sources of supply at one time One person could never be enough for the narcissist They're too insecure They need lots of attention And they will make up excuses to put you aside Too They are punishing you Sometimes the narcissist will push you away Just to punish you and that's all they're really doing when you're not there Maybe you confronted them on something Or you said or did something that offended them So they feel they need to get revenge They feel the need to punish you Three, addictions When you're not there The narcissist will be indulging in one of their many addictions They are dependent on many unhealthy activities or behaviors Such as shopping, gambling, alcohol, drugs, video games and sex It's escapism They're trying to seek distraction and relief From their unpleasant reality By seeking entertainment or engaging in fantasy Because they hate the reality of what they've become Four They're preparing for the discard They're preparing to get rid of you But they're not quite ready yet Because they're still getting something out of it By keeping you in the picture So instead they will ignore you They will leave you in an uncertain one decided state Where you do not know what will happen or when something will happen They will leave you in an uncertain situation that you cannot control And in which there is no progress or improvement While they're busy plotting what they're going to do next They're plotting the next move But they will make up some excuse for you They will tell you they're preoccupied with something But really They're grooming their new supply They're getting ready to advance their new supply to the primary position And they're preparing to get rid of you The more time you spend with the narcissist The more they will begin to see you as the problem They will begin to see you as this person who is causing inconvenience and annoyance And they will try to spend as much time as they can away from you Because you're just a means to an end You're just there for when they need you For when they have a useful purpose for you You're expendable But as long as their bed is first in from being with you They will keep you around But it's not because they care about you It's not because they desire to have a future with you Narcissists do not want love They do not want a relationship They just want someone there to serve them and fulfill their wants and needs They're self-absorbed and they lack empathy They put their own needs before everyone else's Which is why when you're not there They will be behaving in a dishonest way They will be doing or intending to do something wrong They will be indulged in their addictions Because although it may seem like they decide to be alone They can't really be alone Narcissists hate their own company They do everything they can to avoid having to experience that They're always looking for a distraction So when the narcissist says they want to be alone What they really mean is they want to be away from you Because they've already learned you They know everything they need to know about you And they know you figure them out Which is boring for a narcissist They want to be around someone who doesn't know who they are Someone who doesn't know what they're about Because they're able to manipulate that type of person They can impress someone like that They can gain their attention and admiration They can extract fuel from them But they can't do that with you Because you know they're not special You know they have an inflated ego You know they're not about anything for real Which is why they'd prefer it if you weren't there Because you keep bringing reality to them You keep telling them the truth And they hate reality They don't want the truth They don't want to exist in their fantasy world Where they can be seen however they choose to be seen But if you're not going to buy into the illusion You're not going to be any good to them It's like you're constantly holding a mirror in front of them And that is something they don't want to see The last thing they want to see is a reflection of their true selves They want the false self They want the fantasy And if you're not willing to participate in that You might as well be dead Thank you for watching I hope this video resonates with you Please like, comment, share and subscribe If you would like to donate My PayPal link is in the video description Coaching Inquiries You can email me at coachinginarch.tv.uk Thank you for watching and I'll talk to you soon


Before it happened, most of us thought about fossil fuels only when we filled up our cars. Then the whole extraction industry collapsed, and we realized that something more important than transportation was completely dependent on these fuels. That was the food system. We never thought about the fact that from growing and harvesting to processing and transportation, our food was made using fossil fuels. This is the story of a family trying to cope with the loss of those fuels. We have to grow, harvest, and forage for ourselves in this new world. It's called food again. Starting in February 2020, join us for new episodes each week as we try to adapt to this new normal. Think of it as a window into an alternative timeline where fossil fuels no longer exist. Subscribe to our YouTube channel so you won't miss it. You can also check out lowtechinstitute.org for more information.


This paper investigates the performance of three supervised deep learning methods for automated USV segmentation, an autoencoder neural network, AE, a UNET neural network, UNET, and a recurrent neural network, INN. These models use spectrogram data from recordings of USVs to detect and classify the calls. The authors evaluated their performance using a dataset of manually annotated USVs, and compared it against other state-of-the-art methods. The results showed that all three models achieved high accuracy, with UNET, and AE achieving values above 23008595 backslash percent 23008595 percent outperforming other methods. Furthermore, the authors tested the models on an external dataset, and found that UNET performed best. This suggests that these models could serve as a useful benchmark for future research. We are article.tv, links in the description below.


Welcome to Power Up Hawaii, where Hawaii comes together to walk towards a clean, renewable, and just energy future. I am your host, Raya Salter. I'm an energy attorney, clean energy advocate, and community outreach specialist. I'm also the principal attorney of Imagine Power LLC. So today, we're going to take a look at important energy and utility news from Hawaii, around the country, and the world, as reported in the last week. So first, let's take a look at some recent developments in clean energy and clean energy policy in the islands. The biggest story out today, I think you're going to hear that from many sources, and I hope you pay attention to many different points of view. The Hawaii Public Utility Commission has approved utility plans that include massive rate increases for Hawaii rate payers. In an incredibly important development, the PUC has given the initial green light to the HECO Company's PSIP or Power Supply Improvement Plan, which include massive rate hikes for Hawaii rate payers. We've got a graphic that we can show here that will illustrate what this means for rate payers. So here you go. Now I try and stay away from too much in the way of nuts and bolts sort of geek out graphics like this, but this I really think we need to take a look at. So what you've got is projections out on two different time frames. And what we're looking at for the 2026 time frame, more than 44% rate increase for HECO, that means Oahu, 42% rate increase for Helco, that means the Big Island, and 23% rate increase for MECO, that means Maui. So as you look at that graphic, what you've got is upward trends. So let's go ahead and talk a little bit about that. So given the substantial, and we can move away from the graphic, thank you so much. So given the substantial increase in rates forecasted in the report, the Commission is concerned, and they did make a statement in their ruling. So this is what was said by the Commission. The Commission is concerned that the companies have not fully considered the affordability of their plans. The companies have provided only limited responses to the Commission's instruction to analyze customer and implementation risks. The companies do not appear to have evaluated the capital investments, financial commitments, and the resulting increasing rates in the context of affordability to customers and the risk of stranded assets. So I'm going to pause here and talk a little bit about what the Commission's concerns mean. And to be totally honest with you, I don't see the justification for an approval of a plan given that grave level of concern. So what the Commission is talking about is that we've got a massive grid improvement plan, and there doesn't seem to have been enough thought in terms of, what is it going to mean to implement this? What is success and failure going to mean? What are the opportunity costs involved in this plan? What does it mean for the residential ratepayers who pay the highest electricity costs in the entire country? What does it mean for stranded assets? And let's talk a little bit about stranded assets. writ large, stranded assets are one of the, I think, the more controversial issues that happen any time you get a grid transformation scheme when you look at it historically, and I think it's important to look at it historically. So traditionally, a utility makes investments in big capital expenses. This is the traditional utility business model. Big billion-dollar nuclear plants, we're going to talk a little later about how South Korea is abandoning some nuclear ideas for future nuclear plants. Billions of dollars for nuclear plants. Billions of dollars for large power plants, and then they get to recoup that investment from who? The ratepayers, customers, you and I. This means you've got long-term investments that last over our lifetimes, sometimes our children's lifetimes that are in the ground that we continue to pay for. So that is what is at stake from even just the initial push for electricity infrastructure and why it's so important that we switch to clean and renewable energy, so it is important that we do that. But what does it mean to have stranded assets? Well, in most jurisdictions I think actually in every jurisdiction that has an investor owned utility, there are a network of agreements and laws that have been in place since utilities were given monopoly franchises. One of them is sort of a loose deal that universal service, folks are going to get service in exchange for exclusivity in that market. So as we have walked forward with various utility reforms and business model reforms that attempt to incorporate market liberalization into the grid, which is the concept that you can derive competition from the regulated markets. You can derive efficiencies by inserting competitive forces into the regulated markets. At times and in other jurisdictions, this has required that utilities divest of certain assets. So utility is entitled per the law in most jurisdictions where there's an investor owned utility to recoup those big investments that they make. So what happens if the plan is for them to turn directions, for them to turn the boat and do something different? Do you think that we get the money back? Who pays for that big investment that is no longer going to be utilized at that scale that we first thought? We paid for it the first time. Guess who pays for it the second time? Yes, for the most part it is again the rate payer. So again, historically in other jurisdictions where utilities were told to divest of major assets, that meant big changes in their investment plans and that meant very, very large billion dollar payments to utilities because of that opportunity cost or that stranded asset. So much so, but I think in many cases it was considered windfall payments. This happened a lot in the 70s and 80s and quite often it was considered windfall payments and it has been very controversial. So I think it's tremendously interesting and also very, very troubling that we are entering this stage in Hawaii of major infrastructure modernization, a major revamping of the rules of engagement that will clearly benefit, clearly at this point anyway, benefit the utility at the expense of a major rate hike for rate payers without having thought consciously about affordability, about risk, about opportunity cost, about cost to society and cost to rate payers, about the cost to the most vulnerable rate payers in the entire country, the very poor rate payers here who suffer more than any other rate payers in the country. What will a 44% increase in utility bills mean to a fixed income, low income, low income residents say on a law who that this has not been considered holistically yet this plan has been green lighted is, it's really astounding because what we really should be looking at is what are the full costs of this transformation, what are the risks, what are the opportunity costs, who will shoulder those risks, who will get the benefits in a conscious way. And this is something that I think has been done frankly better in some other jurisdictions. Now I have practiced in New York, has the New York plan I think been completely holistic in terms of, in terms of what stranded assets look like, who will pay for what, no I won't save it it has, but has it been clear on what it's trying to do in terms of, look our goal is to build this platform that can include more distributed generation, one, two. Our goal is to split this market up between the utility and the private players and here are the rules of engagement. So this is how this large pie is going to be split between the private sector and the public sector and the investor owned utilities and yes, plans for increased community engagement and environmental justice, has New York gone as far as they should, no. Has New York gone as far as California where they have a major cap and trade program, the proceeds of which in many times go towards community and environmental justice concerns, no. But has there been a discussion, has there been a portioning of the market, is there an understanding amongst the community of regulators and others of what's going on? Yes, does more need to be done? Yes. A undertaking, I think what I'm trying to say is that undertaking this kind of cost is the equivalent of entering into a major grid modernization scheme or plan in Hawaii and that it would be done as an afterthought or as a concern with a lack of planning that this wouldn't be in the forefront of the conversation, I think is a concern. Now I do want to say that I think HIKO has in many cases done a fantastic job of managing the highest solar PV penetration level in the entire country. We know that HIKO is dealing with grid modernization. How can it move on to this next level of grid modernization for Hawaii? And I understand that the commission has also really had to grapple with a lot of issues at times with limited resources. So I don't want to be overly critical. I want anything I have to say to be in the light of helpfulness. I think what would be best if we can really talk about this massive, massive investment. It doesn't look like a massive investment right now, but when you add up the numbers of what 44 percent rate increase means, when you add up the numbers of what stranded assets could mean, we're talking about a major restructuring effort in Hawaii without, I think, intention, enough intention and a conversation about what is the intention for this grid modernization, a restructuring plan in Hawaii is extremely important. So I, gosh, there's so much to say, but I'll go on a little bit and talk about one of the key reasons what this plan is willing to do. And I remember when I came here in 2014 to speak at the Maui Energy Conference, I came because New York was looking to build the specific plan was we're going to build a platform. We're going to build a platform that will allow the integration of more renewable energy and distributed generation. And at the time, we knew that Hawaii was working and grappling with some grid modernization efforts. At the time, I don't think that it looked like the plan was similar. It didn't look like we were looking to do a platform here. But the truth is, is that, is that we were? So what does this grid modernization plan do? What is all of this money in this market, major market restructuring that is really happening kind of under the radar? What does it mean? Well, the HECO grid plan could enable as much as three times more rooftop solar in Hawaii. Overall, the new plan will shift the bulk of funding from physical infrastructure-based wire solutions to grid modernization solutions was really what we're talking about a smart grid with HECO planning to spend only 49 million on wire solutions through 2023. So the utility states the initial focus of the plan is to mitigate existing service quality issues that are arising so as to continue to enable ongoing customer adoption of solar and batteries. HECO also seeks to create a platform whereby distributed energy resources, a broad category that includes not only solar and batteries but demand response to other technologies can help to meet the state's 2045 renewable goal. This will require the deployment of technology both on the customer and utility side of the meter. Unlike earlier plans, which called for widespread deployment of smart meters, in order to save costs HECO is now calling for such meters to be deployed surgically, which will include customers with rooftop solar on circuits that HECO considers saturated and those that are nearing such levels. This deployment will include related software to help customers make better decisions about usage. So like I said, it seemed a couple of years ago that we weren't talking about a platform now that's exactly what we're talking about. So we're going to move to a break when we come back. We'll talk a little bit more about the big HECO plan and other things happening in Hawaii and around the country. I just walked by and I said what's happening guys? They told me they were making music. Welcome to Sister Power. I'm your host Sharon Thomas Yarbrough where we motivate, educate and power and inspire all women. We are live here every other Thursday at 4pm and we welcome you to join us here at Sister Power. Aloha and thank you. Back to Power Up Hawaii where Hawaii comes together to walk towards a clean, renewable and just energy future. I'm your host, Raya Salter. So you just heard me sort of say a whole lot of things about the green lit HECO power supply improvement plan and I just have to say a few more things. We're looking at plans for massive, massive rate hikes for at least for Maui, the big island and Oahu and we're talking about folks who are already paying the highest rates of energy in the country and some may say hey but you know overall folks don't pay as much necessarily well you know what I don't think you get credit because you don't have a heating season I don't think you get credit for certain things. Yes, folks aren't needing to spend a lot of money on heating their homes but that I think is a context that should be removed from the discussion. Energy costs are too high in Hawaii and there are a lot of concerns and the commission shares them about what this power supply improvement plan will mean. So I said a lot of things but I also want to say again hopeful very positive I think the most important really the most important thing to say is that okay Hawaii is on the path towards grid modernization that is going to happen the company has a plan does this mean that the company has been told that it is okay for them to start spending money left and right on the specific plan actually no you know often that's not how these regulatory things work I think and it's the same thing that happened in New York the rubber will hit the road in the rate cases for the for each utility and secession as they come about that's where the rubber really hits the road in terms of specific proposals are made and what is able to be spent. I will talk a little bit about what I think you know I talked about this this what really is a major restructuring and market restructuring plan that is happening under the radar with this PSIP and really what we're talking about if they're going to build this platform and we also talked about it's going to really enable for increased amount of solar and other on distributed energy resources yes that's good that's the point I've talked many times that that you know the state cannot afford for ratepayers to do all of the spending that we need to have private industry and the innovation that comes alongside it playing in the game so we want this to be good for the clean energy industry and distributed energy resources industry we want to find and capture efficiencies and innovation and we want the utility to be able to continue to be you know a big employer in the state an innovator and a just you know a positive force in the community as we move to get off of oil and increase our energy security but we cannot do it it cannot be at any cost it can be not be at any cost in terms of affordability and what does it mean for us to be paying into the system at such a large such a large percentage what does it mean for us to be paying into the system and what do we get in return so what are the community level opportunities for this platform how will residents and other folks who are looking to survive and thrive in OYE as we all know is really really hard what will the opportunities what will the business opportunities be what will the economic opportunities be how will how will various different populations be it racial or ethnic or whatever part of the island that you live on how will people be able to participate how will they have a voice how will it be fair how will folks be able to economically participate in this green energy economy besides only the green energy companies and what will be the environmental and land use and environmental justice and land use justice and climate justice implications of this of these distributed energy resources so what do I mean by that is it okay for for certain folks to use their people to go out and build these distributed energy resources throughout communities one of those resources going to look like here I think we've all on all of our hikes in Oahu and we love hiking and we love getting up in those mountains I know we do what are we doing for most of the time we're hiking up to some busted piece of infrastructure we're going up to something that the military has left we're going up to stand next to some cell phone tower or some old piece of energy infrastructure nobody knows really what it's doing and I'm sure there are a lot of beautiful reasons and we love our infrastructure however what are these assets going to look like who's going to have to look at them can they be designed so that they are not eyesores can we see as these poles and and wires are abandoned that we talked about can we see them going away imagine the roads and the vistas in Hawaii without big ugly poles and wires thank goodness we don't have lots of advertisements imagine if if if distributed energy allows for that to recede this this infrastructure takes steps back where infrastructure is causing potentially a health problem or a visual problem can that be solved you know can we can we actually improve the quality of people's lives and and increase participation in the energy system and and also the biggest question I think where are these assets going to go in terms of land use they're going to there's not a lot of land where will the solar farms go where would the biomass go where will biofuel be planted if anywhere at all this is going to mean there'll be winners and losers do you want to be the person who lives next to a ace a you know a plant a biomass facility do you want to be the person who lives next to that big solar farm and that land has been used in that way when what you really wanted to see was just a clean you know a clean view of the ocean and what does this happen and to whom what parts of the island will be will be given favor will it be low-income folks will it be high-income folks guess what guys not trying to make any villains but traditionally when it comes to NIMBY not in my neighborhood it tends to be low-income folks who end up with the fuzzy hand of the lollipop now why do I go on and on and on about this because this is exactly the work but I engaged in in New York we worked with social justice on poverty groups racial justice groups and we just wanted to enter the conversation how can this benefit everybody and I think what we drummed up was a commitment within the reforming the energy vision process to environmental justice protections now what they'll actually mean going forward will that actually be you know substantive in terms of rules I'm going to say yes because I know that the advocates back home are working hard at it but that this stuff is absent here I think the problem and I look forward to talking to folks about what this is going to mean what this is going to mean is it going to be Hawaii and Hawaii's culture and Hawaii's progressiveness is it going to be a meaningful transition that is just and fair to everyone that makes Hawaii cleaner and more beautiful and more affordable as and all the islands of Hawaii's as a model for the world or are we going to have an unaffordable transition that is going to saddle our young people with extremely high high debts for the rest of their productive lives big questions moving Denver based renewable energy companies Sintek bioenergy has opened its first office in Hawaii the sales and field service office which is located in Honolulu will support local installation of Sintek bioenergy's technology for delivering clean energy through advanced thermal conversion of biomass and other waste materials the company said in the statement now this office will be headed by Dr. Chris Guai who has over 15 years of experience working in the renewable energy industry so we're talking about a punahoe boy local boy who says energy security is a big issue in Hawaii Sintek's biomass energy systems will contribute to the growth of local renewable energy resources and achieving the state's goal of 100% clean energy by 2045 Sintek's biomass systems are powered by a variety of biomass and waste materials including wood chips not shells and fruit pits the systems are housed in standard ISO shipping containers making them easy to transport and install the biomass units are scalable from 165 kilowatt up to one megawatt so the company is currently planning to install install additional units in California Texas and Japan there are currently no specific plans for a biomex system in Hawaii so why did I really want to talk about this one I think it's cool that we've got this what look what a cool energy firm that realizes that you know this particular type of technology biomass can be really valuable for islands so where do they decide to come boom here right at the crossroads between here in Asia they're going to use a local fellow hopefully generate some jobs and some money for folks here to sell some systems back on the mainland and also also in Japan so I think that is super cool another reason why I wanted to talk about it just as I said fruit pits nut shells it's all well and good I'm not speaking to this technology but the consequences of these technologies even clean energy technologies are very significant and as somebody who has been to some biomass facilities something that you want to smell you don't want to be next to and I think we've all experienced driving past some either wastewater treatment blend facilities biomass facilities so there really are consequences to these distributed energy resources and you know what I think I'm going to take a pledge I'm going to stop talking about Hawaii's 100% renewable energy goal I have been an advocate for RPS and aggressive RPS and I celebrated this goal over the past two years with everybody else and I continue to believe in RPS but this I think has turned into a rallying cry for 100% renewable energy without thoughts enough thoughts about affordability about sustainability about resilience it cannot be 100% renewable energy for 100% renewable energy's sake as much as we need to have energy of independence here there are a lot of other conversations that need to happen in that context because as the Commission is also concerned about what are the risks in implementation both in terms of money both in terms of the environment what happens to these distributed assets who's going to be watching the companies that are going to be playing on this what are they going to install who's going to fix it will folks invest in things that just become more of this infrastructure that we hate hike to and sort of try and overlook as we as we both mostly bask in the beauty of the ocean in the clouds will quality of life become worse when it comes to energy here in terms of better and when you think about higher energy rates there's a real trade-off there the last thing I was going to talk about that I'll just touch on for a minute is that at the Verge conference there's a lot of discussion about the culture of Hawaii and how much that culture blends itself towards clean energy and so I think we really need to think is that lip service are we going to have folks come and you know say a few words and we're all going to give a blessing about clean energy and yet it's off to the races without looking at the moral and justice implications of what's going on I think that's a problem and I think that we really need to work on these things that are happening under the radar which of course is what think tech is all about some things happen under the radar here in Hawaii at big tech will take you there so I had a lot to say I hope it was informative in some way this is rya salter signing off for power up Hawaii aloha everyone