Hey, everybody drew here that anxiety guy calm back for another episode with on the other end of the line on the UK Billy from anxiety United say hello Billy. How are they good to be here again? Yes? Yes, this is the second in our little series that we're gonna be doing based on an article. I wrote many moons ago Called dealing with anxiety. The only way out is through We're gonna break this down Billy and I are gonna go break this down kind of section by section through the article and in the Video description whether you're listening on my channel or Billy's channel will be a link to the article if you Want to follow along go ahead and do that. Yep. And what are we gonna talk about today? My friends, mate We are gonna talk about the concept of not being in any real danger Because it's an important topic the fact that We all go through this but essentially there is no danger. That is true So the the the topic of today is fear, right there. Correct. It's all about fear and fear is probably the Fears the driver behind all of this stuff that we're talking about in the end. So the subheading for me was Well, they we don't want to bleed into the next episode, but yes fear feeds that But let's just talk about being in no real danger. I think that that's important. So why don't you get started? The thing for me the no real danger is that it's the fight or fly response. That's the thing that really stands out for me I think with the fight or flight We experience the exact same things that we would if there was a tiger in the car park You know, that's true. The problem being that if we experienced the fight or flight and there was a real danger I don't think that we'd think about how fast our heart was beating or how much air we're taking in because we'd be So focused on dealing with the situation, but I think because it's out of context That's where the problem lies. It's those the physical sensations the symptoms And because there's nothing that we're actually afraid of there It just blows your mind, I guess. That's a really good point because there's nothing to focus externally on So when we get into a panic situation a panic attack or anxiety becomes really elevated We're dealing with fear for the most part fear is driving it and Yes, it's all about the adrenaline dump, right? So once it happens it happens and these are normal predictable measurable physiological responses to the presence of adrenaline in your bloodstream And we have to recognize that it doesn't necessarily mean just because your heart is pumping and you're breathing heavily You're sweating and your legs are jelly It doesn't necessarily mean that you're really in any kind of danger. There is no real danger There's nothing to fight or fly from that's exactly right and you make a really good point Since there actually is no external danger. Nobody has a gun at your head There's no lion chasing you all the things you said you're not hanging from, you know a cliff or anything like that There's nothing to focus that on so you tend to turn our focus inwards on her thoughts and what we're feeling physical physiologically and And that's where the fear comes from yet. There's nothing actually there to be afraid of so how do we How do we recognize that and then how do we deal with it because that's really kind of step one here? Is to recognize that you're not in actual you're not in any real danger Maybe we should go through what we what people seem to be afraid of Okay, so I've made a list of a few of the things or a few of the things that have come to my mind The fear of going crazy. That's probably a big one. It's one of the top two I don't know if we want to go through these as a list and then go through them. Sure. Let's blow So next I've got the fear of passing out, which is a big one for me The heart attack fear of a heart attack. Yes the breathing and suffocation and Then a fear of losing control just completely gone. Yes, and I think when you look at Study after study questionnaire after questionnaire over the many years the top two things that people fear when they get into these Situations are the fear of losing control it losing control and going insane seem to get lumped together Coming psychotic and the other one is dying. So you mentioned like having a heart attack. I think I read somewhere that for females It's the going crazy losing control and the heart attack is the male thing. Is that it seems to be there's no like hard evidence of that But you know, you know Mars and Venus thing who the hell knows I'll never understand those people So if you have ovaries, I'm talking we're never yeah, yeah, we're never gonna figure you out So I probably just had 50% of the population of the boycott our podcast. I'm not sure I'm gonna edit that Yeah, you might want to edit that out So no, I mean you're right. So men and women tend to perceive it differently But the top two concerns that people seem to have and I think we kind of all relate to them was dying or going insane Yeah, yeah, definitely And here's the good news We pretty much know that no one has ever gone insane During a panic attack or lost control or died So I think one of the points that I made on that on the going crazy was that the fact that you know that you're Experiencing all this stuff essentially says that you're you're of sane enough mind to know that this is happening So if you were going crazy, you'd probably just be sitting there and stuff would be going on and you wouldn't even really recognize You wouldn't anything. Yeah.  I was trying to make but I was going all the way around the house. No But that's okay. That's okay. Yeah, crazy people don't know they're crazy. They don't know they're going crazy Yeah, that's crazy as a derogatory term, but I am on thin ice today. What is with me Tuesday morning? I'm just defending everybody getting confident. That's what it is. That's what it is. So yes, no one courage Yes, no one loses control. No one dies. No one goes insane. No one becomes psychotic during a panic attack It just doesn't happen But yet these are the things that we fear and the fear is really generated internally. I think for the most part It's generated by how we feel and the thoughts that we have so we should maybe think about that The difference between a scary thought and which could certainly signal danger, right? I mean, I know for a lot. Yeah, I've heard you talk a lot in the past about negative thoughts, you know I've never know. Yeah, whether it was a sensation that always hits me first or whether it's a thought Yeah, that's one thing that I've always struggled to come to terms with is is which comes first Okay But yeah negative thinking is a is a big issue for me because when I when I get bogged down in the negative thoughts, right? That that's what it is because they tend to start with maybe it's not such a A paralyzing negative thought but they just escalate and escalate and one thing leads to another and then it it's the catastrophizing and that's That's where I feel like I kind of lose control I know that I don't but that's where it becomes just this train of thought that just rolls off Right on its own and it's not that losing control of like, you know going insane or losing your mind It's losing control of your thoughts, right? Yeah. Yeah, it's just getting carried away Yeah, that can be tough and so I think the source of the fear that we're talking about which is the false fear There really is no real danger is the sensations in our body the racing heart the breathing the jelly legs Maybe feeling a little off balance or dizzy. That's a big one for me. I still feel that primarily that's my still the hardest symptom for me to get past and But and then also what goes on our heads So like you said the racing thoughts the negative thoughts see the catastrophizing what if there's two phrases that I always Say that people should probably look out for one is what if and the other one is oh my god When you get to oh my god or whatever your analog is When you get to what if or oh my god, you've kind of gone off the rails and then here. We here we go Here we go right here. It comes here. It comes. Oh, oh, oh is another one And so our thoughts can trigger this can feel this feel this fear our bodies can feel this fear Are there external things? I mean we're talking about the fact that this is fear without any danger behind it Can we think of any external things that actually fuel this fear that bring about this false fear? I don't know whether it this would be class does that but at the moment in the UK The weather's been really stiflingly hot. Okay, and that's that's something for me They're always sets off my panic but that then to be fair It's the it's the air quality, but then it becomes a breathing thing So I suppose the external thing is the heat, but then it's my thoughts of I'm not getting enough air or You know so it goes from that but then it becomes and we get on that snowball thing and that's a good point It's actually really good point because I think we can then have external fear. Yeah. Yeah, I think right But the difference is again even in that situation So maybe it's very hot where you are right now and maybe humid But it doesn't it doesn't mean you're unsafe yet that will trigger this fear thing exactly So it's not so much the the external influence or whatever that Yeah, it's just a little maybe a little spark or something. Yes, and it's mainly how we interpret it So just like anything else. It's how we interpret what our bodies are doing. It's how we interpret our thoughts It's how we interpret the environment around us that I think puts us in this false fear situation I'm gonna full false fear. No real danger. Whatever it is. Yeah, yeah So I think job one that most of us have is we talked about last week job You know job one really is to understand the framework of accepting and courageous being courageous and all that persistence and patience But really I mean you get to the nuts and bolts So which is what we're talking about now The first thing to do is you're gonna have to really believe that the fear even though it feels so real every bit As real as if somebody had a gun is not real. Isn't it the fear is real, but the danger is not it. Yeah Yeah So, you know down the road We're gonna have to talk about a little bit more about that fear cycle I guess and how we're gonna deal with that But really our goal today was just to sort of unmask that Can you think of any times that I mean, I know I can in my own they're embarrassing sometimes if I think about it But you know, hey go on go on for go on share share but Times when you were absolutely convinced that this that there was a real danger But and then you know, it just turns out to be not I mean I could think of many times and for me You know, I never had that fear of going insane or losing control for me It was always a fear of physical damage or death. Yeah, and I can remember Very clearly over the years those times where I let it get over the edge You know the tipping point when it there was nothing you could have done that would have convinced me that I was not having a Fatal heart attack or stroke or God knows what sort of physical thing And we've all wound up right in the emergency room. I've never know You have never done that never gone that far. Yeah, yeah for you. I have done that. I mean, it's embarrassing to me I mean not in many many years, but especially in the beginning for most many people the first thing things you got to run for help You got to run for real help like ambulances and doctors and nurses in a hospital and that sort of stuff I think it's interesting. You've never gone down the road. That's really it's really strange Usually my go-to thing is to just isolate myself. That's how I tend to deal with it I'll usually run to the bathroom and just splash water on my face wherever I am. That's what I'll do With we used to have a service in the UK by the NHS. I can't remember what it was I think it was 111 or something like that. It was NHS direct Okay So you could phone up this helpline and and talk about how you were feeling or whatever and they sort of guide you or if If you needed to go in to hospital and they would tell you right I phoned that once But I think I was waiting for that long that by the time I'd actually got through I'd kind of Yeah Yeah, yeah, so maybe that that was their strategy probably Sometimes it at least here in the US the way it works and we have a lot of those things There's no government-sponsored line like that But there's a ton of helplines and stuff usually in each community each state or whatever But we really do tend to and I understand why this is we tend to err on the side of caution So if you call your doctor at eight o'clock at night Yeah, and you get him on the phone and or her on the phone and you say this is what I'm feeling I've had a doctor say to me. Well, it sounds like you're having a panic attack, but just in case Yeah, you always get that just in case if you're feeling if you know shorter breath You should go to the hospital and they'll tell you the same thing like as soon as you walk in I know in my experience as soon as you walk in they look at you and they know They just know because they've seen it a million times They say yeah, you know So, you know in those situations, I do remember very clearly times when I was absolutely convinced and not only was I convinced I acted upon it as it really was danger And then when I'm feeling very embarrassed in the end So I think many of us have done that the fact that you have not done that. I think It's so interesting because You you will deal with it by isolating a little bit Yeah, yes and and almost then acknowledging even tacitly that that it's generated from in inside Like you're almost acknowledging like well, you know, because if you were having a heart attack splashing water in your face Isn't gonna save you Unless you've invented something new but no, no, but it is interesting Consciously to do that as opposed to go for external help like medical. So that's really great I think I've learned over the years that just allowing the time to pass Although I mean, I'm still obviously scared of the symptoms and the sensations But I know that deep down that if I just It doesn't matter what I do. It's gonna pass It doesn't matter whether I run around the house or splash water or scream for help or call whoever I know I know deep down that 15 minutes down the road I'll start to feel Normal. Yeah. Yeah. Yeah, and that's the benefit of unfortunately for you and I many years of experience experience Yes, you do learn from experience, but you know in terms of the the no real danger of the false fear I'm always fascinated by how you've learned that over the years I've learned it over the years many people that we both personally know have learned that over the years There's some mechanism and I don't understand where the mechanism is that made you learn that or made me learn that or made Chris learn that or the people that yeah, you both know but but other people almost never have that light bulb go off So I know people that are still, you know heading to a hospital when they have a panic attack Yeah, yeah never actually fully accepted that there's actually no danger here So I'm always, you know, that's for some people if you're listening and you're new to this You know, it's this you're just now getting into the getting into like it's a hobby That was that was not the right way to say that but but you're just now first dealing with anxiety and panic and those Things this is probably the hardest lesson to the first lesson to learn the hardest lesson Yeah, yeah, and it's not one that I sub cut that I consciously learn something just But I think like you said it's time. It's experience unfortunately, right sadly We have to have those experiences in this and even though, you know rationally you may know like I'm having another panic attack after panic attack number 10 It might really take until number 30 for you really buy into it because what you think rationally and what you do during a panic attack Are often two very vastly different things Yeah, yeah, but it all comes down to just understanding that the fear isn't real. It's just not real It's not real. I think another part of me me not calling the emergency department is probably embarrassment as well just Feeling like a bit of a doofus Yeah, I have been there and those times when I have done that and I think I've probably only done that three times If I think back maybe done it three times Enough for many many years, but you always I always find up wind up feeling so embarrassed and yeah Yeah, anybody that knows me knows that like I'm stubborn. I you know, I could be bleeding from the head I will not call the doctor like that's just stupid that way But in those situations I ran for help when I really didn't need it. So it was embarrassing, but maybe we should talk for just a minute about Anticipatory like future fear Anticipation which is such a huge part that stands in the way of a lot of recovery for a lot of people and and the fear that comes I call a future fear. It's our anticipatory anxiety. Yeah. Yeah, I call it. I think that's real fear, too But it's also not real. So I mean, it's real fear, but the danger isn't real, you know, we're anticipating future danger I don't know if that if that's something that you have had That's a big one a big one for me Yeah, yeah, because even though as we've just been like I've spoke about panic attacks as if yeah, don't bother me But they do bother me they bother me that much that I anticipate Doing pretty much anything get them in it because I don't want to experience even though I know That allowing time to pass will let the panic attack. Sure subside. I still fear bringing that on I don't want to experience it and I think that's probably what keeps me Personally stuck in that the loop. Okay, because you've got to be prepared to Experience those feelings and learn that the fear is not real. Yes You know, and there's only so much. I feel brave enough in times to put myself through it Yeah, you know what I mean? Yeah, I hear you but and that anticipatory thing I mean, I think in a lot of ways the future fear or the anticipatory fear is what turns, you know, panic attacks or just Anxiety into a disorder. Yeah. Yeah when we anticipate that we may panic or we may have anxiety and we fear how that's going to be We're anticipating future danger that doesn't even actually exist. That's when we begin to modify our lifestyles Worlds get a little smaller. We stop. We start avoiding things people places activities on that, right? And that's what turns just anxiety or just a panic attack because evidently almost everybody walking the planet at some point in their life experiences some form of anxiety or Even a panic attack here and there.   It's like it never happened. So Sorry, yeah, so the future that that false danger that we anticipate in the future is a huge deal So, you know when you know like well, I have a wedding to go to next week out of town And you know, I haven't been out of the house in three months. What do I do? That's that's that future fear that anticipation of false danger. That's That's really kind of driving things. I've missed so many family weddings over the last few years. Sure No, and there's because of anticipation or future a hundred percent Yeah, and there's nothing I'd like more than to go and do it, but it's the fear of experiencing those unwanted Even though I know It doesn't matter. It's just it's the loop.  Eventually it will stop hurting. We know that but it doesn't You want to smash your finger with the hammer? Yeah, this is it. I would do that. Yeah Yeah, so I get that I think it's important for people to understand that it's not just we're only talking about false fear during a panic attack We're also talking about false fear or false danger that we anticipate in the future because When it's happening, that's an event or an episode But when we anticipate false danger in the future, that's what drives lifestyle changes and that's what turns into a disorder And that's a real thing.  I feel like this is a counseling session Maybe it is. I don't know. I'm not complaining. Yeah No, it's good because I feel like I I need to although I know the nuts and bolts and we've discussed it many a time Yeah, it doesn't hurt to take the old tools out the box and You know keep them sharp. Yeah. Yeah. Yeah, sure So I don't I do think we've have we exhausted the idea that the fear is real, but the danger is not these are fake dangers Yes, you are in no real danger.  Okay, so we've gone about 20 minutes I think we should probably wrap it up here. So we don't happy with that. Yeah, that's good Yeah, so I guess we'll end like we're always gonna end if you have questions or comments You could be there's a million ways you're gonna be able to listen to this or watch this Billy's channel anxiety United on YouTube. There's mine that anxiety guy So we'll put all the links, you know, the social Go ahead if you're on YouTube comment, whatever channel you're on if you're listening to this is a podcast on my website By all means comment there and we'll look for comments and we'll talk about them and I should send the comments Yeah, I send them right. I think we said that last time Questions Billy doesn't want to hear. No, that's that's not true. We'll talk about that one day, too I think that whole like discussing it too much thing you and I have talked about that. Yeah Yeah, how that could be detrimental, but sure some of the comments my way. That's fine I'll give you the links Twitter that anxiety guy facebook.com slash that anxiety guy or that anxiety guy calm Like it's my YouTube channel is also that anxiety guy. So where can they find you Billy? I think it is. Yeah, just YouTube YouTube.com slash You know that's it that'll do. That's all you need to know That's good. Yeah, so ask us whatever you want and before we go we got some really did you look at any of the comments?  We got some very nice comments for people There was only a couple on mine. I think I can't remember somebody commented this morning somebody that's watched my 31 days Yeah series and they've been commenting on pretty much every video like I've watched it over the course of the week and They commented on it. Well, we've got very very kind words and we both appreciate that So keep it coming very much. Yeah, very much. We're all here What will I need to learn as as well as everybody else? Hey, I'm learning as we go. So, you know, this is it We'll all pick something up from it. Exactly. Exactly. So alright folks Well, thanks for hanging out with us and I guess we're gonna see you next time. Well indeed. See you dude. Bye for now


Hello and welcome to recon village. My name is Kayla Kaye and I will be walking you through a presentation on oscent for sex workers So for starters, you know 2020 was a strange year. I Have a lot of friends friends of friends who were looking for alternative ways to make money this year So obviously, you know bands took to twitch to try to do socially distance concerts We had people trying to start a podcast But overwhelmingly the way that people found to make money was through only fans or just for fans So as the person that people knew who does security a lot of people came to me and said, you know, how can I stay safe and Anonymous thought that made a good idea for a community project So I thought about it, you know, what are some of the limitations to and entertainers and in committee? So obviously there are some that are harder to change than others You have physical attributes such as physique tattoos birthmarks hair and eye color Additionally your location a big scam that popped up over the year was the Amazon wish list trap Again promotion was fairly difficult because there's a huge Conflict between promotion and privacy They're not mutually exclusive, which I'll discuss, but they're not it's not easy to achieve a balance either Additionally Payments there was the Venmo trap. So these payment platforms, which are also social media platforms and Again, you know stolen images. So finding leaked images and recordings can be very difficult And of course, you know, there's always data breaches. So there are lessons to be learned from things like Ashley Madison So my general answer was if you know how to use open source intelligence, you might stand a chance And I thought in order to explain this it would be good to create a sex worker's toolkit so in working with people throughout the year did a lot of work to help people understand there's a difference between Establishing an alias and just picking a stage name Establishing an alias is much more than just picking a stage name Also using best practices for privacy Doesn't mean that you can't promote but you do have to strike a balance and you can have a lot of fun with counterintelligence tactics and This becomes especially apparent once you learn how to cyber stock yourself your alias and any counterintel that you put into the world So when I say that an alias is more than a stage name When you want to be an entertainer and entertainer you should start by checking your real identity and the identity of your significant others friends and roommates I Usually recommend starting with that's them calm a lot of the services to do this within the OSINT framework Have turned into paid-for services But I wanted to make sure that Anything that I talked about within the sex workers toolkit was free and available to individuals at no cost so If you were to use that tool you'll probably be likely to you'll likely be dismayed to be honest You're going to be disappointed Because you're likely to find your home address Your phone number your email address and social media not just your own but of anyone who's been physically close to you So this is problematic because the process of cyber stocking in a media in a world with social media isn't just about you It's about everyone who's physically in your orbit or On in your orbit online as well so In order to break this out further When you're establishing an alias you want to get a dedicated business phone There can be no overlap in your phone contacts or your search history So when you are deciding to go into this any social media is immediately going to pick up on your contacts and start referring people to you That's very problematic if you're trying to have a hidden profile if you're trying to maintain some anonymity in the world Or at least keep some privacy from certain people who would normally be on your Facebook Instagram Twitter accounts Additionally when it comes to creating a new email You're going to want to create a new email and a backup email You're going to want to make sure that those have Multifactor authentication on them you want to make sure that they have a secure password and If you can use a system with N10 encryption something like proton mail That would be a big plus when it comes to delivering private messages Additionally You want to start by creating a virtual p.o. Box with your staging and you want to use that fake address for all of your new accounts You do not want to create any accounts on only fans just for fans cash app Or anywhere else until you have this step out of the way You want to make sure that your virtual p.o. Box is located in a different city that you live in This relates directly back to the Amazon wish list scam So the Amazon wish list scam is that a lot of people will say that they want to buy you gifts and many genuinely do But as an entertainer when someone buys you a gift off of your wish list, they're at least given your city and your state with and when you combine that with information from your pictures and The social media and promotions that you put out there you ended with a lot of identifiable data that could allow someone to figure out your geographic location in addition There was a scam out there that if you Allowed them to buy you something they could set themselves up as a third party and Amazon releases your actual address information to that third party So scammers would put up the item that you wanted Pretend that they were selling it purchase it from themselves and then they would be given your physical address and location Immediately from Amazon it would be released and they would know where you live This is a huge problem for anyone who's an online in the online entertainment industry Anyone who's working for only fans or just for fans the fine line between a Parasocial relationship and an actual relationship is often blurred. It does not help if Those people who don't understand the difference get your physical address So I can't understate the need for this if you're going to have an Amazon wish list You can't go back and do this step later.  This has to be absolutely separate from anything that you've done previously And the extent to which it needs to be separate cannot be understated So I'll go into some of the issues around photo posting and Some of the stuff that you need to do in order to protect yourself when I talk about privacy But when it comes to establishing an alias, there cannot be any overlap. You cannot friend any of your friends. You cannot share What you're doing with anyone who's in your social circle if you hope to maintain anonymity from everyone Else who's in their social circle All right so moving on Obviously when you're establishing an alias you want to use a VPN you should never reveal your real IP address Your real IP address can be geolocated using open source intelligence tools This means that someone could figure out your exact street address or at least down to a couple of blocks for most services Just using your actual IP address Additionally When it comes to payment platforms a lot of people do private videos Outside of only fans are just for fans. They get to keep more of the money that way This is problematic for reasons I'll talk about later whether it's legal protection or Privacy or ability to take legal action However It is one of the best ways to make money. So when you're establishing an alias You need to set up a cash app if Venmo is linked to your contacts and social group Then you should use cash up and vice versa if Venmo is not your primary one And you're using cash up and you need to switch to Venmo for your business account You should never Share the information between them. You never want to share the social networks on those two platforms Additionally when you're creating a Alias you want to create a fake real you this is for plausible deniability purposes You can go on LinkedIn.  This is all part of the counterintelligence and You can have a lot of fun with that so Counterintelligence will be any challenges around your physical attributes. You can actually address with those counterintelligence tactics You can use Photoshop to slightly change your features. You can get Tattoos and put them where you don't have tattoos. You can cover up the tattoos you do have You can change your hair color You can change your eye color and you can wear a mask. So there are multiple ways to layer these kind of counterintelligence techniques in the real world as well as online So when it comes to using best practices for privacy, this is a multi-part issue So privacy and promotion are at odds with each other In concepts so conceptually There's some real problems there, but in practice some privacy practices are essential to your safety as an entertainer So if you want to stay anonymous, you may be less successful Then if you weren't trying to stay anonymous, that's At this point being quantified It's kind of a known fact of the industry There are phenomena of phenomenal exceptions, but for the most parts The more private you are the less promotion the less promoted you are and therefore Less accessible and you may not get as big of a following But if you're interested in striking a balance between privacy and promotion, there are things that you can do So removing the permissions from your social media apps on your phone on your business phone And making sure to never share your location is extremely important. So I have an example here of geocreepy.com You can go and view all of the locations ever associated with someone's uh social media accounts and in pulling that up Obviously that gives an attacker an entire list of places to meet you naturally, which is um Could be unwanted So obviously it's really creepy. Uh, there are a lot of tools like this, but this one's very visual I recommend you go to geocreepy.com and give it a try I think when it comes to using uh practices for privacy Your past social media can be compared to your promotional media So to put that in perspective if you've taken a photo at a location that you love for your original social media Um changing the permissions on your original account is not enough to protect you So you can use facebook graph to go through any picture Whether it's been whether your privacy settings have been set or not So just by using facebook's own tools you're able to see Uh past items that are in their history and using those past items they may be able to See that it was you Putting a similar post at a spot that you love on your real social media accounts as well as your obviously promoted Social media accounts So this is problematic. You should really take into account the physical location. Uh, there are a lot of efforts to do geolocation Not just through metadata. You should always remove your metadata, but even more, uh, you know complicated ways have been used So as an example, you can go to sun calc dot net Or like a more look at more of the tools on the oscent framework If you go to sun calc dot net it helps to geolocate someone according to The sun's positioning and a photo So just time of day when posted Uh the way that the sun is reflected in the post may be enough to help someone Figure out where you are at least to a relative degree And with additional features that can help them stalk you which is not something that you want. Um When it comes to keeping your social networks You should also keep your social events separate. So similarly if you go to a special invite only event You should not be taking a picture with your private cell phone and your business cell phone to promote uh where you are At the same time just by putting those two things up at the same time that obviously Uh gives positive correlation to anybody who might be using a tool like facebook graph to go through your historical pictures and try to figure out if that version of you on facebook matches the version of you and your uh promotional materials again, um You know facebook's not the only one this can be done with instagram This can be done with tiktok or snapchat or any of the social media platforms You want to be really careful to keep your social networks and social events separate Just even seeing someone in the background of your picture if that person actually keeps the a very public social media profile They'll be able to find you through stalking them to a relative degree as well Additionally uh removing metadata from photos before you store or share them is important to ensuring that your location is not discovered Um, this is a basic thing, but not everyone is aware. They're varying degrees of You know technical skill sets. There are a lot of tools for removing your metadata I will say the one thing that seemed to be the most common mistake in sharing metadata Was not removing the metadata before it was stored. So if your iCloud account was breached Then they could get all of your pictures, which included metadata So you want to go ahead and make sure to restore your metadata. You want to remove the metadata before you even store it You want to keep a copy of the picture that has no metadata on it Additionally, you know a lot of services remove it, but wherever you store it it can be stolen from that location Um, so you want to make sure that you are scrubbing it as soon as the photo is taken all right, so using best practices for promotion so Not just talking about privacy here. Um, we have to strike a balance So there's good news in the oscent world kind of so let me explain what I mean by that Um, you might be grateful to find there's so many social media management monitoring tools. So you have wiki.kenberberry.com As an example, we'll have all of these social media and management monitoring tools Many are paid for but there's still a lot that are free And you can use uh oscent on your competition. So you can create a private list of your competitors on twitter No one will know who you are following. So that allows you to know when they're online know when they're offline um Know when the right time to blast out a tweet knowing how to pick up their followers You can get a lot of um intelligence off of what your competitors are doing without them even knowing Additionally, you can use facebook watch to notify When they're promoting or going online similar for ig You have the same thing for tiktok so That's another way that you can use oscent to track your competition And of course you can set up google alerts to see anything that pops up about a specific competitor online The reason why I say this is good news is you can do it to your competition But they could also do it to you and of course an attacker can use this But this is the level to which even if you're using good privacy practices You are still going to have this amount of information out there So use it to your advantage. Um And hopefully it'll help you with promoting your account And when it comes to using best practices for safety Um, you want to use the platform security if you're on only fans or just for fans There are security options there Never start streaming without at least taking a peek at those security options Um, probably the most important thing you can do is use multi factor authentication on your email and all of your accounts You want to make sure that you never click on links or open files that were sent to you whether it's in chat or email You should never open those files. There's no need Um and avoid clicking on any links just because they can Um compromise the machine that you're on whether that's your cell phone or a laptop So you want to be very careful when you're doing that Um, additionally platforms like only fans are just for fans tie your real identity to your alias And there's nothing you can do other than contact them and ask that they increase their security efforts So unfortunately, this is the part where I said if you know oscent then maybe you stand a chance Even if you were to do everything right and be very Good at what you're doing. Um, you're still at the mercy of your payment platform and you're at the mercy of These platforms that host your content to ensure that they're actually taking steps to protect your privacy and your safety So what's next for me over the next year? So two interesting problems relating to oscent popped up over the last year Um, number one banning an account is not the same as banning a user making moderation 10 times as hard as it should be I think there's room to create an oscent tool and I've been uh working on that with another woman that I invited to help me with the project And The second thing is that most money is made off of private recordings Which lack licensing and tracking to prevent piracy If you have someone who uses fraps to record without your consent Only fans and then upload it to another adult site. You can use the only fan lawyers to send them a Notice that to send the platform that they uploaded it to a notice that it must be removed But your only ramifications are legal ramifications through the only fans platform. You have no other way to Get these recordings off if you privately provide them to someone So there's definitely some work to be done there The biggest challenge is finding out where your image has been uploaded If they didn't specifically use your alias or your stage name. It's going to be very difficult to find um, and even if you do find it Obviously you'd have to reach out to a lawyer or work with someone to get it taken down um, this leads to a lot of entertainers using Uh watermarks on their videos and watermarks do lead to a lot of complaints. So Well, there are image recognition tools Like roboten Out there. They're not very good at this point There's definitely a lot of work being done in the space and a lot more That can be done So I hope to come back with some interesting tools next year And in order to help me build those tools, I invited Jay Lynn Denise. Um, she's going to be running the twitter account She's a developer. Uh, she's got experience in the industry and she'll be able to Help me with all of the cyber security questions that everyone has been sending So you can go to the modestyproject.com or you can tweet directly at her Let her know if you've uncovered any other scams or have any other questions And uh, we hope to speak to you soon. Thank you


of the Organization Committee, it's Professor Edgar Alden from ICTP, and he will give us an introduction about martingales in non-equilibrium thermodynamics and their applications. So thank you very much for having you and the floor is yours. So thank you very much Jan and all the organizing committee for suggesting my talk to be included in the program. Today I will briefly or try to briefly summarize recent work that is a review on how to apply martingales to stochastic thermodynamics, which is a recent trend, a line of research works that we developed over the last five, six years. So this is the main reference, martingales for specifics. It is a very, it's a tutorial review, not a book. It's very long, 300 pages. I expect it has around 3,000 erratas, so whoever reads the review and finds a type of, we welcome feedback. Here are the collaborators in this review. It's Rafael Xamich, Simone Frank and Ken, and most of the results that we review here are, let's say, belong to this recent trend in applying martingales to thermodynamics, in which we have these two very first contributions, I believe, in the topic. So I will try to give you an idea on basics on this topic and also on how can we apply for there, we'll get new fluctuation theorems and new ideas in stochastic thermodynamics. So there will be a structure in this way. So first there is an introduction, very general of martingale theory. Then there's a big block on how to apply this in stochastic thermodynamics in different situations. And we have also classical applications such as in finance, population genetics, or applications in other domains in physics, and it's mainly dedicated to patient and dedicated students. So we include also mathematical proofs, all the examples, such that you can take it as a course on the topic and learn slowly. So I have divided the content on how to navigate in the review in two ways. First, these are the old tricks for new docs. So what should a new student learn about this or can a new student in the topic learn from their view? So we have, for example, a list of symbols which is three pages of notation, which can help you to write the thesis because notation in stochastic thermodynamics is tricky. There are basics on martingale theory with examples applied in physics, so not just mathematics. We have also basics on stochastic processes, basics for Markov and Langevin. So it's very, very self-contained, I would say. Also, basics on stochastic thermodynamics, such as the first and second laws which were reviewed by Massimiliano and Hugo the other day, etiorems on martingale theory. So this is a course material for mathematicians, and also the classical applications in finance and population dynamics. This is like for a newcomer to the field, but there are also new tricks for all dogs in the sense that if you have been working for a while in the topic of stochastic thermodynamics, you can make use of martingales for deriving new universal results, which you can get, for instance, in non-equilibrium study states or in driven processes. So there is really a collection of techniques that you can you can find by applying martingales, and this is what I will try to explain today at this, the most basic ones. We also have all the records, so there are two chapters that are very technical, but for most mathematically oriented, you can go there and check on the details and also applications in other fields in physics, such as quantum or spin class. So I will try to begin to introduce you to the martingale by considering an example that probably you all know, so it's just a unidimensional diffusion, over time diffusion, in which we have a potential that may change in time following a protocol plus an external force Ft. This makes a total force to be defined by Ft, and this in the presence of a thermal bath that induces Gaussian white noise fluctuations. You all know that at time t, you can solve the density of the probability density for the particle following the Fokker-Pank equation, and that since 2005, in work by Udo Seifer, it was introduced the notion of the non-equilibrium system entropy associated to the particle being next at x t at time t. The average of this quantity, I remind you, is channel-centered. So an important notion in stochastic thermodynamics is how this system entropy changes in time. In a small time interval, the position of the particle evolves following the Langevin equation. So you know that at the time t plus dp, the value will be x t plus the increment, which is given by just integrating the Langevin equation. However, it was not so clear until around 2005 how the system entropy evolves in this interval, given that the evolution of the particle was Langevin. So you may ask, how does this object change in t to t plus dt? You can hear, say, okay, this object depends on x and on t, and apply the chain rule. So partial of this with respect to time dt plus partial of this with respect to x dx. This is called the standard calculus, chain rule, and in stochastic calculus, this is called stochastic, sorry, Statenovich calculus. So you do this change in t plus dt, you get into this equation, which has two terms. One is f times four times velocity, so this is the heat dissipated to the environment, the environmental entropy, and the rest is understood as the entropy production. So whatever is not coming from exchange with environment, we say it's a production term of entropy. This was already introduced in the classic paper by Eul Cipher, but something you should notice is that all these calculations were done in the Statenovich convention. So what if you take this equation and you write it in ito? It should be just, let's say a mathematical exercise, and 12 years later, we show that this equation becomes this sd in ito, which seems to be as complicated as the one in Statenovich, but it has a very particular structure, because in particular, you see that there are two terms that look very similar. This term is the square of the noise amplitude here. So if you are in non-equilibrium stationary state, partial t is zero. The first term is zero, and the change of the total entropy in a small interval has this beautiful form. It has a drift term and a noise term that is in ito, that has the same amplitude. There is a square root of the same thing, where this is the current and this is the density of the time t. So you can take these two equations, one is for the dynamics, the other for the thermodynamics, the process and integrate them, and this will give the fluctuations of entropy production. Please notice that you need to specify how x evolves in time, so this equation, and that the stochastic entropy production depends on what is the evolution of xt. Moreover, the bt, so the white noise that appears for the entropy production is the same as the one of the particles. So this is a very compact form and, moreover, this quantity here, which we called back then entropic drift, is stochastic, so it depends on where the particle is visiting, but it's always positive. So there is a stochastic positive drift term in the evolution of stochastic entropy production. So this type of decomposition appears quite a lot in martingale theory. It is called the dupe Meyer decomposition. So it means, first of all, from this equation, we can show that the entropy production, stochastic entropy production is a sub-martingale. So whatever is the history that we observe of the process at two times s, the conditional expectation in the future is always greater or equal than the value of time s. This type of inequality you can show directly from this formula, and whenever you have a sub-martingale, you can decompose it in two terms. One of them stochastic and increasing function is this integral of v. So it's the first term times vt. And the other term, which is, it is an ito integral. So this term has zero mean. So whatever is the evolution of the process, it has zero mean. So this is also what it's called martingale. So this is just pure noise, in other words. Another interesting manipulation is if you take this equation and you do a change of variable, you go from s to exponential of minus s. So this is a change of variable x to e minus x. You can apply ito's lemma and go from this equation, sd for s, to this equation, which is an sd for e minus s. Importantly, e minus s doesn't have a term like this one times dt. So it has only a noise term. So it's something that depends on xt times noise. And this is in ito. So it means that this has zero mean. So e minus s, it's called martingale. It has zero mean. It has no drift. This means that if you look at the stochastic process, up to time s, you know this information of the process, but you don't know the future. There are many different future histories. Then what you know is that the expectation in the future of the e minus s is going to be equal to the last observation of the process. So you don't expect to grow and you don't expect to decrease. This is called martingale property or e minus s. It's not the typical martingale property you see in mathematics books. The process itself is a martingale with respect to itself. Here is, you have the dynamics and you have the thermodynamics. So you condition over the dynamics and you observe expectations of the thermodynamics process. This is a central result in our theory. You say this martingale condition for e minus s. And you can always show, this is explained in chapter seven in the review, that any convex function of a martingale is a submartingale. So minus log is a convex function. The minus log of e minus s is s, is a submartingale. You expect whatever you see, you will see in the future and the expectation in the future is going to be greater than the current one. So interestingly, this generalizes the integral partition theory because you can set s to zero and you have this condition x zero and then average over x zero and you get the integral partition theory. So this is a consequence of the martingale field. And moreover, the second law, you get it from the submartingale. You set s equal to zero and you get a second law. So this is very insightful, very fundamental, I would say, but you can get more results from here. It's not that martingales are just to understand the process of time t, but they can be applied also to first passage quantities, as I will explain later. Moreover, the decomposition that I explained, you may ask, how general is this? Well, I show you for one-dimensional systems, but you can have also multi-dimensional systems like colloidal particle interacting with many active swimmers or a single particle with many degrees of freedom. This can be described by a more, okay, d-dimensional Langevin equation with possibly space-dependent noise. In that case, you always also get in steady state the same type of equation. Here I miss a t, where you have a drift term that is always positive and depends on the currents and the diffusivity matrix. So again, you get the same structure. So it seems this result for the martingality of e minus s is more generic. So it's not just for universal systems. Moreover, there is an interesting technique applied in martingale theory and also in finance, which is called the random time change. So up to now, I've shown you how entropy production changes in time, but in the normal time. So you have a clock and your clock is deterministic and every time t, you advance one second now. So this is the evolution of entropy production in steady state with a normal time. And now let me do the following trick. So I will start measuring time in a different way. So I will start measuring time by weighting it with this quantity, the entropic drift. So I look at my system and when the system is dissipating a lot of heat or producing a lot of entropy, my clock starts to run faster. I'm just multiplying this quantity. So I'm evaluating this quantity along the trajectory and multiplying my dt. This is what I call entropic time. This is, of course, an illustration. But it's quite interesting that you can now do a time change in this equation. And it becomes just this very simple equation in this entropic time in which this is a drift diffusion process with drift one and diffusivity one. So it means that processes that have very complex dynamics like the once stationary non-equilibrium process is to example they show here. If you measure time in these units, they all become or the platicians of entropy become as those that can be obtained from a particle in a ring with d one and b equals to one. So this is a bit was quite remarkable for us when we were doing research in this topic. And you can show this, illustrate these examples. If you look at the fluctuations of entropy production up to a time t equals to one, the distribution is typically non-Gaussian. For example, if the particle is drifted in this periodic potential, it stays a long time in this minima and the entropy production at a fixed time has this structure with peaks. This has been shown also in experiments. You do experiments with a colloidal particle in a periodic potential or you have a single electron box or electron jumping in and out from a box. You compute entropy production and you see distribution is typically non-Gaussian. So this is a bit of urban legend. So entropy production fluctuations in general are non-Gaussian. However, if you scale time, so if you use this entropy time and you wait until the entropy time reaches a given amount, all these models, the distribution of entropy production at the entropy time equal to one is Gaussian with mean one and the facility one. So you can get it by solving this simple model, which is a particle in a ring. It's quite striking and we are not the only ones to find this. I'll show you later, also in the housekeeping entropy production, you get the same property. But this result is very insightful because it tells you that all statistical properties that are independent on time contractions or delays should be universal. So for example, the global minimum of entropy production does not depend on when it happens. So it is a quantity that does not depend on your scale of time. So if you compute the distribution of the infimum of these three different models I showed in sketches, they all have the same distribution and this distribution is the one of the particle in the ring. But there are infinite properties like this. There's also the supremum before the infimum or the number of times the reproduction crosses an interval. These do not depend on when it happens. These are universal properties. You can see a review in chapter five or chapter seven in our review. Moreover, this nicely composition into drift and diffusion term, it allows you also to compute non-universal quantities such as, for example, the final factor. The final factor is not a universal quantity. And you can show that from the question I showed you before, you can get an uncertainty in quality for the entropy production. It is equal to two plus the variance of the tropic time divided by the mean. So this looks like an uncertainty relation because this is always greater than zero. So this is always greater than two. But you can get directly the final factor of entropy production by computing the fluctuations of the tropic time, as I showed here. Moreover, you can extend the result to non-state line process and get an extra term that is basically depending on a correlation between the system entropy and the entropy drift. This is a bit more complex to understand, but it has some similarities with a very recent work, which is called the variance sum rule for entropy production, where they computed also exact expressions for the variance of a non-equilibrium process and split it into terms. Some of them depend on this math calligraphy case, depends also on correlations between force and displacement. It is a bit of a particular case of these ideas, but they should be a relation between recent progress in the field and this result that we have in the past. As I said, this can be also called a variance sum rule. So we are writing the variance as a sum of different terms. So all I've shown until now is for stationary states, but there has been progress in non-states in my states. For example, in this work by Chun and Noh, Piardin 19, they showed that the housekeeping entropy production for any non-equilibrium process, so this can be also driven, has also the same structure. So it's also exponential marking it for any non-equilibrium process. Also, we showed that the entropy production is general, not an exponential marking it when you have driven process, but you can find a compensator. So find a process that is an exponential marking it, which is just the entropy production plus something else. And I talked about this in a previous work, so I'm not going to insist on this, but this is useful to derive Yershinsky's qualities at stopping times. So when you first cross a threshold, so you are not looking at fixed time, but stopping times, also design gambling demons. And there has been also more advanced progress on how to find martingers in a general equilibrium process to derive, for example, green cubo formulas for non-marketing process. I guess Hong-Kian will talk about this during the conference. Moreover, we are working also on a case where you are out of equilibrium, but you also have unidirectional transitions, which is a bit of a pathological case. And in that case, we find that the non-adiabatic entropy production is a key concept. But this is a bit technical, I will not talk about it today. I guess we will have a draft sooner or later, probably, in the archive. So I will continue my talk by trying to rationalize why there exists many martingales under many phases of the second law regarding martingales. By presenting you what we call the Tree or Football Club of Second Laws, it is a bit of an advanced topic, but it is essential to understand our theory in full regard. This is a hierarchy of second laws, meaning that one of these generalizes the next, which generalizes the next. They are very strange names, but these strange names mean different degrees of conditioning. So conditional, strong second law, strong second law. I will explain this in a bit. And they also have a bit of esoteric names concerning this lambda sigma, because these are specific functionals of trajectories, which have a given form. And depending on the form, you can get as particular cases, the work, the entropy products on housekeeping heat, et cetera. But most of these results are generalizations of lactation theorems that already exist, whereas others give to new results that I will try to introduce to you at the end of the talk. So in this Football Club or Tree or Second Laws, most of the results are well known, but there are a couple of them which are new, presented for the first time in this review. So one of the key features of these laws is that there are generic in the sense that they apply to both Van Jeevan and Markov's Jam processes, and they only have one key assumption that the ratio between path probabilities is well defined, in the sense that you cannot have cases in which the log of this ratio diverges. So this in a very mathematical way, it means it's called absolute continuity. So if the probability for a trajectory in the process is zero, then the probability of the trajectory in the reference process, which we will use for calculations, should be also equal to zero. So typically, this Q is the probability in the time reverse process. So this is, in other words, meaning micro-reversibility. So you see the forward and the reverse trajectory with non-zero probability. Anyway, a big result, a key result in deriving this hierarchy of laws is the fact that ratios of path probabilities are martingales. So if you take the path probability of a reference process Q divided by another path probability of your process of interest P, so I have a physical process, it has a path probability P, and I will consider another random whatever other process that has another path probability Q. So if you do this ratio and you compute the conditional expectation given the history up to time m, you can show that when you average this over P, this is equal to r at the time m. So this is a martingale when you average with respect to the probability P. This is a two line calculation, but one has to be very careful, and for the reason I will explain in a bit. When you find such a martingale, it is quite nice to realize that if you apply a convex function to Rn, any convex function of a martingale is a sub-martingale. So this is the same thing I explained for e-minus s. If you do minus log of e-minus s, then you will have a sub-martingale. So you can first prove a martingale for e-minus s, and from this immediately follows that s is a sub-martingale. Moreover, as you can show here, if you put this expression here, you have this type of inequality, which looks like Kullback Leibler, but it's more detailed than Kullback Leibler, because you are not averaging over all P of xe to n. You are doing an average with the conditional expectation, so you have this type of averaging. So this is what we call usually a conditional strong second law. We know the process up to then, and we expect in the future is what we're doing, we're calling conditional strong second law. If you put m0, you will have Kullback Leibler, so what we know very well from the foundations of the field. Okay, so this is what I'm just showing here. This we call usually second law without the css. This is conditional strong second law, and this we call second law. Moreover, here is an important message to all of you that this martingale, martingality property, is not so generic when you look at processes that are not time homogeneous. So for steady states, this works for equilibrium. If you start in equilibrium, this works. But if you have a time in homogeneous dynamics, such as a relaxation or a driven process, this is not going to work. And this is a central message of our review. So you cannot just say that q over p is a martingale. You have to be very careful and check case by case. In the case, the dynamics is not time homogeneous. Moreover, these are a bit more details, but this is just to introduce you to the notation. There are two classes of functions that we consider. One is called sigma, which has p over q evaluated on the reverse. So this is a typical form that entropy production has it as probability divided by the probability of the time reverse trajectory. And this could be a time reverse dynamics, but there exists a second class of functional that are more simple. It's just the probability to see the trajectory in the process divided by the probability to see in another process the same trajectory. So without time reversal, one particular case of this lambda functional is the housekeeping heat for adiabatic introduction introduced by Massimiliano and Chris Vandenbrock. So there exist different families and these events are important because the lambdas are always martingales, but the sigmas you have to always have a compensator. Moreover, there is even a worse creature or a monster, which is what we call sigma d functionals, which are a generalization of the sigma. So here what we are doing is we have a process p, which evolves from c o to t, and we look at the probability, it's a marginal probability in a subinterval r s. And we compare this to a q process in which we look at the time reverse trajectory, but time reverse with respect to t, but in the subinterval t minus s, t minus r. This is a bit of a complicated creature, but it's very fruitful because from it, you can get most of the results from 10 years ago in stochastic thermodynamics and what concerns second loss. So for example, if you put in the q process, you put the time reversal and you take the r s interval is the full interval, you get the stochastic entropy production, but you can get other interesting quantities. What was very surprising to us is that this object has this interval, it will say, okay, this is just pure mathematics, but besides that, with this interval, we show that the process is submartial with respect to forward time and supermartial with respect to backward time. So it conditionally increases, when increasing time and conditionally increasing when looking backwards in time. Again, this is very recent, so we are still not fully sure about the interpretation, but we have one result I will present in a minute, which may, we are looking for feedback to try to get, you know, what does this mean, okay? This is very, very recent. You have five minutes. Very good. Five minutes and done. Yes. Great. So a particular case of this p and q could be that you have a process p and starting at the initial density rho zero, and then you look at the same bulk dynamics p, but starting from a different initial density. If you do that, this sigma g object becomes a very easy to understand quantity, which depends only on the current time density. So this is the log of the density of the process p at time t divided by the density of the process t at the same time. Okay, there are two processes and you evaluate the density at the same time in the process. So this implies, among other things, this very well known result, historical second law that appears in Thomas Cooper book, for instance, and other results. For example, we can use this to prove that the non-equilibrium free energy in a relaxation process is a backward sub martingale. This means that if in a relaxation, you see trajectories of particles or the system in the future, so you see how they evolve in the future, you can predict the expectation of the past. So this is different from the classical second law, which we say in the future, entropy will increase. Now we say we look at trajectories and now we know where we come from. So we can say that in the past, the particles of the system on average at a higher non-equilibrium free energy. This is a totally new result and your feedback is extremely welcome. Okay, I should start closing. So I just presented one part, which is fixed times, but martingales are really good to extend ideas to stochastic times. This is already an idea that was exploited by the Nobel laureates in economics, black and skulls with fair markets. This I explained in other words, so I would not enter into this. This has many applications for biophysics and also solar cells and to extract, for example, extreme values and survival statistics of the work. And this can be extended to non-equilibrium to dream process, but I have no time for this. The main message is that there are these second laws, there's the hierarchy at fixed times, but also the hierarchy at stopping times. You can look at the particle until it crosses a threshold and measure the dissipation from time zero until you cross a threshold. So this hierarchy exists also for stopping times. So there are two football clubs in the end, one of the fixed times and the other stopping times. So there are two hierarchies, even though maybe it's not clear yet in the reading. I finished by announcing an archive, a mission this week about stochastic thermodynamics of particles in fluctuating fields, and that fields can locally extract heat from a bath when you drive a particle out of equilibrium. You can take this week. We are also working on other topics, bullfrogs, hair cell bundles, for example, this is a making, but this will be part of future talks or discussions. And I end up acknowledging my collaborators in the quest of Martin Gels, my group at ICDP and funding. Thank you very much for your attention. And this is for students. I have three courses that you're going to see on YouTube that could be useful for you to get introduced in the field. Thank you very much for your attention, and I hope I'm not out of time. Thank you. Thank you very much. That was a very nice talk. You were just on time. And now we have time for questions. The general rule for questions is that the junior attendees will be given priority. So if they are junior people, PhD student, master students, young postdocs, please raise your hand virtually by this reactions button and clicking raise hand, and you will be able to ask questions. In the meantime, there is one question by Tom Aldrich. So yeah, you can unmute yourself. So please ask. Hi. Thanks for the great talk, Eka. So do I understand properly that if you're in a stationary distribution, non-equilibrium steady state, the Martin Gail approach is always going to work. But if I'm in a system in which there's a time dependent, my Hamiltonian is time dependent, or I'm in a system where the Hamiltonian is constant, but the system is evolving, the distribution is evolving, it's not guaranteed to work, but it might do. Yes. So I totally agree. So if you start in a stationary state, the exponentiating negative entropy is Martin Gail at all times, and otherwise it is not, but you can still find a process of this Martin Gail. And the process is not E minus S, it's E minus S minus an extra term that is related to the fact that the density at stopping times is not the same density as what you will get if you don't stop, if you don't have a first-party criterion. So let's say entropy production is not Martin Gail or not some Martin Gail in the driven process or time dependent, but you can still find a Martin Gail, which is your... Okay, but whether or not that extra term is easy to interpret is the key question. Yeah, actually, this extra term is not difficult to interpret because it relates to the asymmetry of the process at stopping times. So when you average it, it has this form. So it's the logarithm of the density of time t compared to the density of the conjugate time of the process. This is related to the work by Van den Brog, Kawaiians, and Barondo in 2007. I don't know if you remember the dissipation, okay, the phase-space perspective. So what they showed was that the dissipation of a time dependent process is related to how different is the phase-space density at time t with respect to the phase-space density of the time-reversed process at the conjugate time in tau minus t. I don't know if this is PRL plus and seven. So in this case, we have a similar result. You have to include also this asymmetry in the process, the asymmetry of the forward process at the stopping time with respect to the backward at the conjugate time of the stopping time. In the steady state, they are equal, so there's no difference. So for details, I think paper with Matano, PRL 2021 is where we first found out to extend it to the driven process. Chapter eight in the review. Thank you. Very helpful. Thank you. Are there any other questions? I see. So Tarek? Yes. Can you hear me clearly? Yes. Okay. Just so when you mentioned that at steady state, any ratio of, if I recall correctly, functions of trajectories will be a martingale when you define our log ratio of, oh okay, it's not the log ratio, it's just Q over P. It's a ratio. It's a ratio of any function of trajectories at steady state. Well, it should be to the two path probabilities. Oh, path probabilities. Both of which are stationary. Okay. Okay. So I'm just wondering if this generalizes the sequential probability ratio test, like walled results, because what happens there is that they consider the log ratio of two path probabilities conditioned on two different hypotheses, and then you get decision times. This is a very good question. And actually, walled sequential probability ratio test is for IID processes. So it's, in the end, it's like stationary. So you are drawing the numbers from a lottery, but this is a stationary process. And indeed, the first time we came up with the results that inspired us to do this research to martingale, at least Isakneri and I, was when we started to work on walled decision tests. So we have an article from 2015 where we had no idea about martingale theory, but we were looking at very similar questions. So in particular, how long you need to wait until you have with some confidence, you can decide whether a movie is running forward or backwards in time. So it's a decision making process to be optimal in decision making, you have to measure probability ratios. So if you want to decide optimally on the error of time, you should do log of the probabilities with respect to the error of time. And then what you get is you should measure entropy production if you want to be optimal. So it's related to one. Yes, IE. But what I'm saying is this it's more general. So entropy production is the log ratio of forward versus backward path. But it's more general. Yeah, that's why any, any two things you want to distinguish will be a martingale at steady state. Yeah, that's why there is all these hierarchies, because some of the things here is not entropy production, it's just probability ratios. Okay. So actually, yes. So this one is always martingale with respect to p. And you don't need that it's related to thermodynamics at all. So you're right. Yes. Then the beauty for the community at the end is to set, to choose p and q that are related to a physical process that you can do in the lab or, or that makes sense to do the study on equilibrium. But you can do finance if you want with p over q. That's why there was all this research by black and skulls and a field of quantitative finance. So yeah. Okay. So I think that we are just on time. So thank you Edgar again. And the next