 If you say writing zero is an erasing process, then I think that's essentially the same. So if you write all the memories just zero, zero, zero, zero, then I think it is essentially the same as erasing. You think it looks like a violation of the second law? Yeah, right, right, right. So I mean, yeah, so you see that. So by erasing, by erasing the system, actually the system entropy production is lowered. So it looks like violation, but we have to pay some cost here. So by adding these two, then, yeah, then the thermodynamic second law is not violated. This is which are ruled by Fokker-Bahn equation. Then you might be likely to use the Wasserstein distance because you visit some connection without the transport theory, what's the idea behind this? Yeah, I mean, the Wasserstein distance is about the distance when one distribution to move to another distribution. What is the optimal way to move from one distribution to another distribution in a continuous long-term existence, for example. So I mean, this is a connection to the problem. What would be the natural one in this context? I think heat or work, I mean, they are, I mean, the right quantity we have to care about in the thermodynamic system. So is it a function of, that's a function of. Wasserstein distance? The state. Function of two distributions, I mean, from one initial distribution to final distribution and which one is optimal cost to move from one state to another state. That's a function of distance between points, right? Yes, right. Why? Yes, right. I mean, for deriving this speed limit, I mean, it is easy to use a total variation distance. That's a definite, I mean, reason why we use the total variation distance. But I mean, I'm a little bit confusing about your question, but that's, I mean, actually that's the Wasserstein distance is some kind of some optimization problem. So I'm a little bit confusing, but it is probably related to the form, okay, okay, here, okay. So if, so we can, we can actually, I can't, I'm now still in on, this is actually kind of ongoing study, ongoing project, but anyway, we can, we can, I mean, probably change this total variation distance into the Wasserstein distance, but a little bit different form. So I think in that form, actually, that there is some entropy production term there. So I think this Wasserstein distance is kind of probably there isn't, I'm not sure, there isn't, probably it has no unit. I'm not sure, but it will have, I mean, the expression have, additionally, it has some entropy production. So I think probably about Wasserstein distance, in that case, the long-term dynamic case has probably no, no unit, okay. Multiple resetting means with different time difference between them. We are resetting the system multiple times with different time difference between them. Then our entropy will be same for its states or there will be different interactions. So you mean that multiple erasing means the sequential erasing or? After the time difference, tau maybe erase the system, erase the system. Then again after some time tau prime, we again erase the system and then again the dynamic goes on and then after some time tau double prime, maybe I again erase the system, this kind of thing. So then in this kind of protocol, we will have the same kind of entropy production rate or different. Oh, so you mean like some kind of a sequential way of erasing process. Yes, so the thing is that I assume that when I calculate this one, when I calculate this total variation distance, I assume that initial distribution is given half and half probability. So if after one erase and then if you do a reset again, then the thing is that the matter is that whether the initial state has this probability. If it changes from this half and half probability, then it will give a different number of total variation distance and then it will give us some a little bit different bounds. And then this is the, okay, so it's still a time and then both to the hotel will be waiting at 6.30, right? So okay, so let's see tomorrow again. Bye. I didn't go to school, but I was at the Overdamp office in Lanzibar, and I was looking for speed, and I was thinking of what to do with this, so I was thinking of the time and bounds, the bounds of relaxation time. The bounds of time, the bounds of relaxation? The relaxation time of the house. And then you come there. Let's go. Okay. Mic. Okay. Okay. Okay. Okay. Okay.