Summary What is life-lecture: Jeremy England (Youtube) youtu.be
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Jeremy England Well, thank you very much, for Coming, to this talk today, it's really wonderful to be here in, a very lovely city that I've never visited before and 1 that, Has some significance for me personally, actually, because although my name is England, my family's name actually used to be England. So I'm actually half Swedish. And I've never been to Sweden before. So I had a wonderful time exploring the city a bit this morning, and I'm really grateful for the chance to be here and share some of the work, that's going on in my group with you. So, where should we start?
Jeremy England I actually couldn't resist the temptation to modify my slides A little bit after my walk this morning because I had the chance in the Gamla Stan to encounter a very striking, specimen of Swedish design, which I wanna show to you because I think it it it's a little bit thought provoking. So I don't actually know if this was designed by Sweden or other people, but this is some kind of little robotic thing with a magnet on its nose, and it is somehow attached to a ball and it's just running around in a box. And I think it's pretty clear to us that this thing is not alive, and, we wouldn't have much of an argument about England yet, you know, I think it's also worth mentioning or pointing out, about this little contraption that There is some sense in which it mimics life more than some things in the world. So if I compared it to a rock, I would say there's something a little bit more like Something that's alive in this system, which is just running around and rolling around, but doing so in sort of a nonlinear way. So there's something a little bit like life about it, but I think the reason that's not interesting to us is basically because This is a contrived resemblance.
Jeremy England We start off with a living thing, and then we make up some little aspect, that we can put into some, artifice of ours that should resemble the living thing. And so it's not very impressive that it resembles life any more than a statue might or Something else we could construct. But then I I theory also that there's a different kind of way in which sometimes things in the world can maybe resemble life. And I thought since I'm visiting Sweden here, I I should borrow a little bit from Norse mythology. So I I think it's a very Striking insight, and I'll be able to make this argument to you a little bit more so at the end, or maybe some kind of deep intuition, that was contained in The Norse mythological idea that the first life came from frost as it formed.
Jeremy England I may be getting this wrong, but at least according to what I read, There's this idea that hoarfrost and salt crystals were sort of the start of everything, and then somehow along came a cow England everything else came afterwards. But the question is, what is different about the way in which a complex structure like this that we see in the world, which I would say we'd all agree is not alive, but somehow resembles the organization of life a little bit more than Perhaps a rock we might pick up off the ground. What is different about this kind of resemblance than the 1 that we saw in the previous slide where someone just made something that they covered with fur and it's gonna run around in a box. And and hopefully, by the end of the talk, we'll be able to start reaching for that. I mean, this is not essential that you you buy, my plug for Norse mythology, but I I thought at least I would mention it because it's a a little bit of an interesting idea.
Jeremy England So How do we start off? I think it's very important in in this subject to be a little bit philosophically careful and remind ourselves of how words get their meaning in the 1st place. And I would be 1 who put forward the thesis, which is not my own, but others have argued this in the past that words get their meaning from their context of usage. And so I don't, as a physicist, want to look for a definition of life that comes from physics. On the contrary, what I wanna say is We have the word life, and we know how to use it.
Jeremy England And there are lots of things in the world that we point and we say, yep. That's definitely alive. And so we start with this Empirical phenomenon are the way we use this word. There's this collection of phenomena in the world. We see them as all being alive.
Jeremy England And now we can start to analyze what are the properties that these things tend to have in common with each other. And when we talk about the world in the language or in the Framework of biology, we tend to focus on things like behavior, evolution, survival, reproduction, heredity. These are the natural categories for biological reasoning. But then a point I think is quite essential to make at the outset in this discussion is that If we instead think about a way of talking about the world like a physicist might, what we find is that We can say a lot of different things about the same system because we're using a different taxonomy instead of categories, etcetera. So as physicists, we could look at the same thing, the same collection of particles.
Jeremy England But instead of seeing a living thing sitting in some water, We might instead say there are a bunch of different locations of particles and distances between them and periods of time that pass between when particles are located 1 place and another, and we're counting things. We might be measuring things like energy and temperature. Although energy, if you look at the units, is really constructed out of more basic things like essentially accounting of particles, time, and distance. So physical reasoning is really rooted in a few very simple categories of measurement. And the point I wanna make is that a priori, Life is totally absent from our description of the physical properties of the system.
Jeremy England So physics doesn't make any distinction between particles that are in the whale and particles that are in the water around it. It's all just a bunch of positions and momenta. And, presumably, there's some equation of motion we could write down That is a good model of how they evolve over time. And whether we're looking at something that's alive or not is not something I would argue that Those basic physical descriptors can tell us. So then where do we go from here?
Jeremy England What I would like to suggest to you is that means that if we're gonna do biophysics and do it well, we have to be aware of the intuitive act of translation that we're engaging in between these different languages of categorization. So just the same way you can do a good translation from 1 language to another or a bad translation from 1 language to another, So there is some sense in which we can correctly or incorrectly map from 1 way of looking at things to another. It is also the case that There is some relevant way of talking about a system biologically and physically and drawing sensible connections between those 2 perspectives. But I think we all can also appreciate that there's no perfect translation from 1 language to another England that there always is a role for the intuition of the interpreter in deciding What is a good translation? So the example I like to present of this in the grand tradition that physicists have of endangering cats in their thought experiments is that you could go to the top of a tower and you could throw a cat off the tower.
Jeremy England And if you wanted to, you could measure how fast the cat is moving when it hits the ground. And that is a simple physical property that you can measure in such a system. Or looking at the same experiment, You could do a different thing. You could throw the same cat off the tower. And instead of asking how fast it's moving, you could ask whether it's alive afterwards.
Jeremy England Right? That's a biological question. And I think many of us can appreciate that how fast the cat is moving when it hits the ground is quite relevant to the question of whether it survives the ordeal. So it's not that 1 has nothing to do with the other. And yet, what I wanna put to you or at least what I would like to remind us of is that it is never going to be the case that asking whether a cat is alive is the same as asking how fast it is moving.
Jeremy England Right? Our choice to relate these 2 2 things comes from our understanding of some kind of intuitive mapping between 1 way of describing the system and the other that At the end of the day, if the cat is in more than 1 piece afterwards, it's probably not alive, you know, that kind of thing, that we need to do do to hook things together. And I don't wanna suggest to you that this kind of experiment is on the cutting edge of biophysics research at MIT, but I think it's it's helpful at least for us to, start thinking in these terms a little bit so that we don't get too confused when we start talking Physics and biology or physics and life at the same time. So now we have to start thinking about what is special about life in terms of its physical properties. That's what I wanna motivate today.
Jeremy England I wanna do physics and talk about physics, and there will be some parts that are a little bit technical. I know this is a very diverse audience scientifically. And so parts of this talk will be more technical, parts will be less technical. Hopefully, everyone will get something out of it. The starting point is to say, how do I take living things and try to be as specific as I can about what physical properties they have that are distinctive of life.
Jeremy England And when I say distinctive of life, that's not the same thing as being unique to life. Theory, I don't think, will ever be A physical property that you could identify that is only gonna be true or recognizable in a living system, but couldn't be realizable in something that you would look at and say, I don't think it's alive. But I think if we can develop enough of a physical understanding of How various lifelike physical properties emerge, we will get a better understanding of how a living thing might make sense as the outcome of a physical process. So here are a few different things that I could start to think of specifying as Physical properties in a well defined sense that I think are quite connected to our idea of what is alive. Every living thing we know of Self replicates, that it can make copies of itself.
Jeremy England That's already a pretty abstract concept. It's not basic physics, but it is at least more formalizable In physical terms than the general idea of life, sensing and computation and anticipation are also things that living things generally do, that They have environments around them that change, and they respond to those changes. And as biologists, we recognize how those responses are Functionally valuable, right, that it helps the organism survive or reproduce or etcetera. So there there's some sense in which The behavior anticipates perhaps something about the future and tries to get into some new configuration that is more suited to that future in some sense. And another thing which is probably the most brass tacks physical thing that we could say, but we don't often think about because we have a different way of talking about it that's easier.
Jeremy England But all living things, I would say, are particularly good, in some sense, at absorbing work energy from their environment. We have to be a little more specific later on about what we mean by that. But just, in a in a rough sense, when I say work, this is a very general category of things. So it could be chemical work or it could be physical work. So there's work if I take a plant and I shine light on it, Then there's work that's being done because there's an oscillating electric and magnetic field, and there are molecules that vibrate in that field and change their state as a result.
Jeremy England You're absorbing energy from a time varying field. That's 1 way of doing work. So plants have to get work done on them by the sun in order for them to keep Running around in their dynamical space in the way that they do. They're also are sources of chemical work. So when a monkey takes a banana off of a tree, it's Finding a source of chemical work in its environment, that's a very abstracted reach from a basic idea of work.
Jeremy England So we're just gonna talk about time varying fields today because I think it's Easier to connect that to our intuition for Newtonian physics, but really this can be writ large in in lots of different categories of work. And 1 of the things I think is pretty generally true is that when we try to understand these things in the biological context, we tend to see the England third Special things about life as being the result of this first property. So we know about the idea of Darwinian evolution, and we Have a pretty clear idea that if you have diversity in a population of things that copy themselves England that diversity in morphology Or in function somehow alters the ability of 1 or another of these forms to make copies of itself, then the thing that's better at copying can do so faster, takes over, and in the future, its traits are more represented. So that's the Darwinian idea that's saying that that has being a better self replicator is going to help you become better represented England take over the world, so to speak. And I think that when we look At these categories, to the extent that we see sensing and computation in living things or absorption of work from the environment, we take for granted that Being better at eating makes you better at self replicating or being better able to sense changes in your environment helps you survive and reproduce.
Jeremy England So we explain these 2 things as being the result of Darwinian selection as a mechanism that arises out of the fact that we're dealing with self replicators. But I think that a priori, you can look at these 3 different things and say they're all different types of phenomena that as we look at physical systems, we could just look for any of these theory. We don't even necessarily have to know what the mechanism of emergence of 1 of these things is in order to notice it and characterize it. So that's what I'd like to point towards is how are we gonna start thinking like physicists, but talking about the emergence of these properties and systems as Physically evolving systems. And I think 1 of the reasons that that's an exciting opportunity is because There is something perhaps a little bit unsatisfying about thinking only in terms of the Darwinian mechanism when we're trying to make a full Picture of all the different diversity and function form that we see in the biological world.
Jeremy England And what I mean by that is that it is easiest to think about fitness a Darwinian sense, when you're comparing 1 finch to another finch, right, they're basically the same whether there's a bigger beak or a smaller beak. It is much harder to think about things in terms of fitness when you're comparing a blue whale to the plankton that's, you know, growing in the water right next to it. Both of these things are very well adapted to their environment in some sense. And it's easiest easiest for us to understand that in terms of comparing this blue whale to other whales Or this plankton to other plankta plankton, not plankta, but, and I think that at the same time, when we try to compare them to each other, it's sort of an absurdity. Right?
Jeremy England There there's no sense in which A blue whale is more or less fit than algae. And there's a whole lot more algae in the ocean than there are blue whales. Even though every whale is very heavy, there's a whole lot of algae if you put it all on 1 scale. And, you know, I think it's it's kind of limiting or and no 1 would say that algae are more fit just because there's a whole lot more of them, and it doesn't do justice to the fact that the whale is very highly functionally adapted to its environment in very distinct ways, to the plankton. So if that's the case, then now we have to start thinking a little bit more about how do we understand evolution.
Jeremy England And I know many people have thought about this for a long time in the biological context, but what I really wanna go for is the idea of adaptation viewed in terms of the physical properties of the system. So we wanna construct some kind of idea of that as we go forward. So these are some questions that are motivating us. 1 is, is there a general language for Defining and understanding adaptation in physical terms. And do we always need Darwinian selection in order to get that kind of adaptation?
Jeremy England Because, clearly, although whales and plankton are very different from each other, both of them are self replicators. And so maybe you always just have self theory England it can get very diverse, but we explain adaptation by that mechanism. And then also, I guess the third Question here sort of emanates from these 2. Can we, in some sense, explain the emergence of lifelike organization using fundamental physical assumptions, and focusing on the physical properties of the system of interest. So this is the answer I wanna give to the first question, or at least this is what I would like to suggest to you might be the case, and you can make your own judgment.
Jeremy England I would suggest this answer for the 2nd question, which is part of what I'm excited to tell you about. And then I don't really have anything too grand a claim In this 3rd case, until we reach the end, and then we can start seeing whether we're moving in the right direction. So here are a few hints that should set us on our way. First of all, here's some things that are true about all living things As a category of stuff in the world that we think have things in common. All living things are made of matter.
Jeremy England They need to eat. They give off heat, and they can't grow backwards. All seem like pretty trivial statements except perhaps the last 1. So what do I mean by that? All I mean is that watching this movie run forward, It may take longer than this, so that it's it's sped up, but it still looks much weirder once you start running it backwards.
Jeremy England And imagine a plant that is all has lots of leaves going back into the seed in the ground and running the reverse movie. We don't tend to see the reverse of this movie. We tend to see the forward direction. That's true of every living thing that as soon as you run the movie backwards, as a whole, this macroscopic object, it looks absurd in some sense, and and you would never observe it. The reason that's interesting, and many have made this observation before, is because when you think about Newton's law, so if you assume if we're gonna assume moving forward that we're looking at matter and so it's made, of stuff that it's effectively modeled by Newton's laws.
Jeremy England And I know Quantum mechanics makes things more complicated, but all claims we're gonna make here are essentially gonna be the same even if we try to complicate our picture in that way. So let's just talk about Newton's laws. Newton's laws have a very basic symmetry in them that is easiest to appreciate when you talk about 1 coordinate. So say my coordinate is the position of the cat. We know that cats can fall down.
Jeremy England So they start with 0 velocity up here and they fall, and then when they get down here, they're moving with some some speed. And then we know that if we flipped around that Speaker, so instead you take a cat and you drop kick it up in the air, so it goes up in the air. I'm not actually this mean to cats in real life. These are thought experiments. So and the cat will fly up in the air, and then it'll have 0 velocity up here.
Jeremy England So What these 2 different trajectories reflect is that there's a symmetry where I can always take 1 trajectory that obeys Newton's laws, I could flip around the velocities at the end, And then I'll just run backwards along the same track. That's called time reversal symmetry. And the reason that's important is because it's saying that Fundamentally, we think if we're dealing with Newtonian matter, for every trajectory that looks like it's running 1 way, we should be able to see the reverse movie also, and it's not forbidden according to physical laws, Which immediately tells us that in principle, seeing a plant run backwards into the seed is not forbidden by Newtonian motion. And that now raises the question why we don't see it. So if it is the case that anything that goes up can come down or Anything that goes up can come down, then why should it be the case that when it comes to biological organization, We tend not to see things run 1 way as much as we do the other.
Jeremy England So 1 of the things that will Light the way for us is thinking a little bit about chemical equilibrium. And that is because there is something that We learn when we first start studying chemistry, that we take for granted a little bit, but comes from this physical symmetry that we were just talking about, Which is the idea that you have what's called detailed balance at chemical equilibrium, which comes from this time reversal symmetry. So what it says is I have if I have reactions and I can go from a to b or from b to a and I can go from c to b or from b to c, That at thermal and chemical equilibrium, my forward and reverse rate for any pair of transitions, a to b versus b to a, is always going to be what determines the ratio of the equilibrium concentrations. So equilibrium constants have this relationship to rate constants. And what we don't usually think about because we're maybe a little young when we learn about this is that that's not the only situation that could look sort of like an equilibrium to us.
Jeremy England So for example, I could have a set of reactions where you strongly and rapidly go from c to a and from a to b and from b to c, but running around in the reverse direction is not so likely. And that is a condition where there could be a steady state where the levels of a and b and c don't change, but where there's a net flux around in a circle from these different chemical Speaker. So that it would not be the case at equilibrium that the forward rate times 1 concentration would be equal to the reverse rate times the other concentration for every pair. Because of time reversal symmetry in Newtonian motion, this detailed balance breaking is forbidden at thermal and chemical equilibrium. And so we start to think about pairs of reactions, forward and reverse rates always matching.
Jeremy England So now the question is, what are the consequences of that principle, and how does that change once we start thinking about Nonequilibrium theory, because something I haven't stressed until this point is that living things are very much not at thermal and chemical equilibrium, England that is part of what is essential to making them as interesting as they are. So 1 of the things that, is suggestive when we think about this detailed balance condition is that it actually tells us something about the non equilibrium dynamics of the system. So if I have a system, England let's say it's in 1 microscopic arrangement that I call I, and then there's another microscopic arrangement called j. And I can think about in some period of time the likelihood of going from I to j or from j to I. And I'm I'm talking about likelihood now because I'm imagining I'm in contact with a thermal bath, so it's at some temperature.
Jeremy England And that thermal is gonna cause what appears to be random motion in the system. If I think about the forward and reverse probability going from I to j versus j to I in the same amount of time, The detailed balance condition we just talked about requires that the forward and reverse rates have a ratio that's fixed by the energies of these 2 states. That's something you get from the fact that at thermal equilibrium, this has to obey what's called the Boltzmann distribution, where you have an exponential distribution over states, in their energies. Something that I think is not usually stressed about this though is that when you look at the ratio of these rates and you know that it's equal to this quantity, what is the exponential of minus beta, which just the inverse temperature times the change in energy. The change in energy, if I'm not driving the system in any way and I'm just fluctuating from 1 state to the other, By conservation of energy, if I have 1 energy in I and another 1 in j, the difference between them has to be the heat that I put out into the thermal bath as I go from 1 to the other.
Jeremy England So what that means is that this quantity can be rewritten as the exponential of the heat exchange with the bath divided by the temperature that I'm living at. The reason that's important is because already what this is telling us is that if I talk about forward Probability versus reverse probability, the probability of going from I to j versus j to I in the same amount of time. What controls their ratio is this quantity which is the heat that's exchanged in the forward direction. The heat exchange divided by the temperature is something we have had a thermodynamic term for for a long time, which is the entropy change in the surrounding bath. So this is entropy over here, and this, I would call irreversibility.
Jeremy England The ratio of the forward and reverse rate, the more so that is a big or small number, the more so you tend to go 1 way more than the other. And so the statistical irreversibility of something happening has a direct quantitative relationship to the entropy that's produced in the surroundings. This is true right now for a system that's not being driven in any way, and it's just relaxing to thermal equilibrium. In principle, it's been possible to make this for a while given what we've known theoretically, maybe it has not been emphasized in the way we usually talk about the meaning of this equation. But what has not been known as broadly until more recently is that this relationship between statistical irreversibility and entropy production remains exact according to Newton's laws with an additional modification.
Jeremy England So now I have this time varying field. I'm somehow Changing the way I interact with the system over time. I'm hitting it with a hammer. I'm shining light on it, something that oscillates or or modulates the force on the system over time. And as I do that now, I still can talk about the probability of fluctuating from I to j versus j to I because of the thermal fluctuations.
Jeremy England But the fact that I'm driving the system now makes it so that every time that happens, I could generate a different amount of heat in my surroundings. The reason being But now work goes in from the drive, and I don't any longer have this conservation principle that tells me that I know the heat just because of the starting and ending energies of these So you can think of it like friction. If I'm moving this glass of water back and forth on the table, then every time I do it, Actually, I generate a slightly different amount of heat because of the exact arrangement of the air molecules that are bouncing off of it in the room while that's happening. So what I do is I average the exponential of this entropy production over all the different ways that could happen, and it still remains the case that the statistical irreversibility is related to entropy production. So this is something that was recognized, by Gavin Crooks in the late nineties and has since helped to contribute to a real Renaissance and the theoretical understanding of far from equilibrium systems.
Jeremy England And this is the principle that we're gonna be working with today when thinking about physical consequences. So the thing that we wanna do now is build this up to a description of the macroscopic arrangement of the system because part of the problem that we have is Microscopic arrangements are not things we can measure. I have no idea exactly where the positions and momenta of every single atom in my laser pointer is right now. I'd like to be able to make some kind of general statement about its properties that doesn't require me to know all that information. So I wanna coarse grain, as it's called.
Jeremy England I wanna Collect together a bunch of different states and call them the same according to some measurement or observation I would make about them. So you do an arbitrary construction of a macro state where you say I have a bunch of different states and I just label them. I say, this state would look to me to have a certain quality and this other state would look to me to have another quality. And once you do that labeling Of all the different states, you can group them together England you can construct an arbitrary probability distribution over each set of states. So you start with some distribution over states.
Jeremy England You evolve in some arbitrary drive over some finite amount of time. You end up with some different distribution over states. This all can be constructed fairly generally. And what I wanna emphasize here, is something that I think was best expressed long time ago by Ludwig Wittgenstein, which is a a quotation I really like, which means the borders of my language determine the borders of my world. So what does that mean?
Jeremy England That what that should emphasize for us is that usually in physics, we're accustomed to doing this coarse graining and saying, this is the position of some end of a polymer at some time, and this is the Evolution at some later time, it's a different location. There there were coarse graining states in such a way where they correspond to measurable quantities, numbers that we're assigning to the system. But it doesn't have to be numbers. It can also be any kind of categorization or classification that you're doing. So I start again with this collection of particles that could be a blue whale sitting in water.
Jeremy England And until I classify the states England I say, this arrangement of these particles would look to me like blue whale and this arrangement of the particles would not. I have not layered my own description of the world on top of them or basic physical description. The reason I think that's important is because it reminds us that as physicists, we have to look at any system and think about, As it's fluctuating around, all the different ways you could arrange the matter in the system. So I could start with primordial or other kinds of soup, and I could talk about after some amount of time In a drive and in a fluctuating environment, what's the probability that you get bacteria living in there? And the point that we sometimes miss is that Any given quality I see in the system, I see a certain kind of living thing there that I have defined in a cert in a certain way.
Jeremy England If I take the atoms in the system and I randomly rearrange them in space both in terms of their momentum and their position, I'm not necessarily gonna still get something that I would ascribe the same quality to. So particularly, if we took a person and we put them in a blender and shredded them to their constituent atoms and they were all arranged in space, would probably get arrested. But if that were left aside and we just thought for a moment about what what we had as a result, it would be very unlikely to look like a person to us. So it tells us that something about living things generally is a very special subset of arrangements that are available to the matter out of which they're made. And now we need to start thinking about why it is that we see organization of those components in particular types of arrangements given all the different possible arrangements that are available.
Jeremy England So where can we take this? Well so first of all, 1 of the things that, we worked on in my group is just Trying to take this idea about irreversibility in entropy production, due to Gavin Crooks and others and build it up into thinking about macroscopic descriptions like I've been talking to you about. And it turns out the simplest intuition in terms of extending this idea, is correct, which is that if you have a macrostate Of any kind that you've specified England you're driving it with shining a laser pointer or hitting with a hammer or whatever you want, and it's also in contact with a heat bath and it's Fluctuating and changing its shape over time, then you can define forward and reverse transitions between these macroscopic descriptions. And if you know these probabilities, they're still related to entropy production in the same way, averaging over all the things that could happen. But now we have to look at total entropy And not just the heat that we exhaust in our surroundings, let's say, because now we have to think also about the organization of the internal parts of the system.
Jeremy England So how big how many different arrangements are there that would satisfy condition 1, and how many different arrangements are there that would satisfy condition 2? So when you lay all this out, I am going to risk giving credit to a very good idea for someone from Denmark while here in Sweden. But There is a really, excellent mathematical tool that you can use to appreciate some of the consequences of, This relation and many others that are like it where you're averaging exponentials of things, which is that because of the behavior of mathematical functions, you always have this inequality that holds. So you can immediately take this result and turn it into an inequality, which turns out to be a generalization of the second law of thermodynamics, that we generally think about the total entropy change has to be positive for a spontaneous process. But now we can say something A bit more useful even perhaps.
Jeremy England We can talk about the statistical irreversibility of an arbitrary macroscopic transition. England the more irreversible it is, the more so we're likely to see something run forward rather than in the reverse direction, the larger and more positive the lower bound on the total entropy reproduction has to be. So the more irreversible something is, the more you have to increase the entropy of the universe. And that turns out to be, an interesting and useful idea. And why is that interesting?
Jeremy England Well, first of all, this is something that has popped up in various descriptions before. So for example, A long time ago in the sixties, Ralph Landauer had a paper where he was considering how much heat you have to exhaust into your surroundings to erase a single bit of information in a computer, which is not something that you initially appreciate as an issue. But if a computer is fluctuating at some temperature and it's made of stuff that obeys Newton's laws, Then if you want to erase information in the computer, you basically have to put that information out into the surroundings, and the way you do that is by exhausting heat. So the Landauer bound is 1 special case of this more general statement, And there are other points that 1 can make. The 1 that we have focused on in my group in the past is thinking about self replication.
Jeremy England Self replication, I'm I'm gonna just treat very quickly a simple idea that you have 1 England it's capable of copying itself into 2 things. I'm aware That whales don't actually reproduce asexually, at least have not been observed to. Maybe deep in the water, they figured some way of doing that. But, Nevertheless, the same idea is going to apply with modifications, or you can think of this as a whale shaped bacterium if you want. But in any case, We have these different physical parameters we could measure about this process.
Jeremy England So there's the internal entropy change associated with the self replication event. There's the growth rate, the typical rate at which it happens. There's the dissipation, the surrounding heat production or entropy production in the surroundings, and also some probability of seeing it undo itself, which we tend not to see, so this is gonna be a very small number. But suppose we knew these numbers. It would be generally the case as a consequence of this generalization of the second law, that we just saw that you can write down a relation which tells you That if you look at the ratio of the growth rate and the degradation rate of this self replicator England the internal entropy change associated with its evolution, that allows you to set a bound on the dissipation, on the heat generated by the whole process and the surroundings.
Jeremy England Or also it could be chemical dissipation. It depends on how you wanna define your problem. What's interesting about this is that if you now return to the idea of Darwinian selection, it so happens that it's the case That if you're trying to make a Darwinian replicator that reproduces as rapidly as possible given Some set of constraints on the durability of the material it's made of and the organization of the system that's required to generate it, then you can grow faster the more so you generate more dissipation in your surroundings. So there's a clue here Because it so happens, it seems like being very Darwinianly fit has a relationship to a particular physical property, which is that you have to somehow dissipate a lot of energy in your surroundings in order to win this game. But this could be some kind of coincidence, or I don't wanna say coincidence, but but at least it's not so easy to generalize this immediately to talk about Self organization and driven systems in general.
Jeremy England The way that we do that is by backing up a step. And instead of talking about an inequality, We are gonna talk about the equation that we wrote down for the general relationship between entropy production and irreversibility. But we wanna flip this around. And instead of thinking about a to b and b to a, we wanna think about the choice between going to b or c given that you start in a. So you start in some random macrostate construction or not random, but arbitrary, however you want it to be.
Jeremy England And after some finite amount of time, You can talk about the probability of generating a certain amount of entropy in the surroundings going from a to b or from a to c. And it turns out that you what you can write down, and this is broken apart heuristically, but it's essentially the same statement that we've seen before With a few simplifying assumptions that we don't even really have to make, but it helps us write it down in this way if we do. We can break the the probability of going to b versus to c apart into pieces that are informative. So this, Although it may not be easy to recognize is the generalization of the quantity of free energy for an arbitrarily driven System evolving over a finite period of time under an arbitrary external driving field. That if we wanna know how much more likely we are to go to b than to c, What we care about are 3 or 4 things depending on how you think about it.
Jeremy England First of all, what we care about is the obvious thing. What I would call the order or organization difference between b and c. It remains the case that all things being equal, it is easier to do something disorganized rather than something organized. So the intuition of entropy as being a tendency towards disorder, is a very common 1, is what's relevant here. That if b is many, many, many more arrangements of the world than c, then it is easier to hit that target than it is to hit the other So it still matters how organized you are.
Jeremy England You're under pressure to become disorganized, all things being equal. But now you get a term that doesn't appear in equilibrium thermodynamics, which is a kinetic term. And what it tells us, and this is not very intuitive, but it tells us That as we go from a to b versus from b to a, we can compare the likelihood of doing those 2 things. And I'm more likely, all things be equal, to go from a to b, if I also am more likely to come back from b to a. So how do we explain that 1?
Jeremy England Well, so this was the point about the entropy difference internally. To think about the kinetic difference, Intuitively, what we're just talking about is activation barriers, and we'll talk a little bit more about this in a second. But essentially, I'm just saying that if I lower the barrier from going from a to b as I Thermally fluctuate, I'm more likely to go in both directions. I accelerate the reaction from a to b and also from b to a. So if you put an enzyme in your system, for example, it's intuitive.
Jeremy England You lower the activation barrier. You speed up both reactions. So this term is just telling us it's easier to go somewhere if it's easier to come back from And then we have this last term. And this is the 1 where it gets exciting in some sense, although I think all of it has to be put together to really get the excitement to make sense. This is the log of the average of an exponential of something, which is a little bit of a complicated quantity, But you can break it apart again heuristically into 2 pieces.
Jeremy England There's the average, and then there's all these other terms that come from the fluctuations about the average. And they pull in opposite directions mathematically. So if you wanna make this term big, notice that in order to be likely to go to b instead of to c, what we're really trying to do is make This thing, much more positive than that thing. So then we're talking about increasing the average amount of entropy production in the surroundings on the way from 1 place another and suppressing the fluctuations. So what I would call that is we're trying to reliably increase the dissipation.
Jeremy England We're trying to Generate as much dissipation in our surroundings, but in a reliable way, meaning that all the different ways of getting from a to b have to have this property as much as possible. So if there's way of dissipating a lot as you go from a to b, but another 1 where you don't dissipate so much, the 1 where you don't dissipate so much really kills you because of the fluctuations about that average. So why is that interesting? Well, first of all, I think it's important for us to understand intuition. And now I get the opportunity to give credit to a Swedish scientist so people can celebrate.
Jeremy England So we're going to think about this, from the perspective of are separated by some activation barrier between them. And I wanna think about a reaction going back and forth. So there's a forward rate from going from I to j, And it's controlled by some time constant that's specific to the system. But then as I lower and raise this barrier, it's also gonna be controlled by the height of the barrier and the temperature. So I have this exponential dependence of rate on the barrier height.
Jeremy England And now you can imagine, what does it mean to oscillate an applied deal. What when you're driving a system, what you're doing really is you're changing the energies of different states in the system. That's what it means to bang on something with a hammer or shine light on it or whatever else. And I'm going to present to you an all things being equal comparison where the point is to understand why dissipation is related to being pushed in a certain direction, Why it is you tend to go to places where you dissipate reliably. So this is a very contrived example.
Jeremy England The blue bars are showing you how the energies of these states oscillate. And what I imagine is I start over England then I have 2 different places I could go. I could go over there or I could go over there. And because of the way I'm driving the system, It so happens I don't really oscillate this transition state or that state. But over here, I do.
Jeremy England And what's more, it so happens in this case that there is this in sync oscillation of these 2 states with their energies and an out of sync oscillation of this 1. So when this 1 goes up, so does this 1. But when this 1 is going down. These are going up. So the reason I've done this is because what this fixes is the return probability.
Jeremy England September, we said the probability of coming back somewhere matters. So the return probability from here is always gonna be the same as the return probability from there. The reason for this is that We always have a barrier height of this delta e in when we're coming back. Right? So going going from this state to there, That can that barrier height can change.
Jeremy England But going back from there, you always have delta e. And because of this difference and that difference, you always have a delta e. So what does this look like? Well, we start at the beginning of the drive cycle England we're over here, let's say. And now, we're oscillating the energies and we get lifted up here.
Jeremy England As we do, this energy drops down. So thermal fluctuations suddenly experience a very low activation barrier to move us over to this transition state. And as we drop down from high energy to low energy, we generate some heat. So our energy went up. So we had work done on the system by the external field.
Jeremy England And then we drop down to this lower energy state, and we generate a lot of heat as it happens. But then when we oscillate the energies of the states more Coming back the way we came, you always have this fixed height no matter how much this goes up and down. So returning is not as easy because of the drive as going over is. And what that ends up meaning is that you dissipate more heat on the way from here to there than on the way from here to there, reliably so. And, also, the return probability is the same.
Jeremy England So you're more likely to go here than there because the drive dramatically accelerates the rate of transition over to this state. And as it does so, it must increase the amount of dissipation in the surrounding bath, that there's more heat being generated in the surroundings. So what we're saying here is that on a surface of states of fixed return probability, you have a very strong coupling between dissipation and drift. You're drift in the direction of something where you do a lot of energy dissipation in your surroundings. Why is that interesting?
Jeremy England We have to get some more physical intuition from simple systems. Here's a very simple system. This is the not the first thing maybe we learn about in a physics class, but maybe the second 1. The simple harmonic oscillator. So we have an oscillator that is driven well, I I haven't gotten to that point yet.
Jeremy England So let's say I have a spring, and it has a certain spring stiffness, and it has also a mass connected to it. There's immediately a natural frequency for the oscillation of this oscillator. And what I can do is I can drive it now with an oscillating Force, a time varying field that has its own sinusoidal frequency, which is not in principle the same thing as omega 0, but We've all seen that movie, the bridge, that waves back and forth and falls down. There are certain frequencies in any given system, where when you drive at that frequency, you see a strong response because when you drive on the natural frequency of an oscillatory mode, you get a lot more motion. And the reason that's significant is because what is work?
Jeremy England Right? Work is the integral of FDX. It is motion with force. So if you're gonna get more work done on you, you have to be moving more. And then once you get more work done on you by conservation of energy, you can dissipate more.
Jeremy England Right? Because you put more energy into the system, you can deliver more out to the surrounding bath. So what we're saying here is that of all the different ways you could arrange your system, You maybe have a tendency to arrange it in ways that will somehow resonate with the external fields so that it moves more, so that it absorbs more work England dissipates more in the surroundings. This is a slightly oversimplified description because it gets complicated when we start thinking about the structure of the end state that we expect as a result of some tendency towards resonance, you could have more resonance, and it could lead to different consequences in your system depending on The exact rules for how the particles interact. But the basic intuition here is that not every driving frequency produces the same amount of dissipation in the surroundings of this resonance phenomenon.
Jeremy England And so particular arrangements of the system that oscillate with particular natural frequencies have an opportunity To relate differently to the surrounding time varying environment in terms of how much work and dissipation they reliably generate. So taking this back to our system, the idea now is to think about you change the driving frequency that you're applying here And think about, am I more likely to go from b to c? And how does changing the time during environment affect which state b versus c is going to be more likely? So now how does the property of our time varying environment affect the organization that we tend to see emerging in the system? So you see how we're starting to drive towards this idea of adaptation.
Jeremy England Right? We're defining a time during environment, and now we wanna know how the structure that emerges reflects a property of in that environment. Why is it that that structure forms and persists as opposed to another 1? Why is it that you see blue whales in the ocean and not cows, let's say? So where do we go from here?
Jeremy England Well, as long as I'm in Scandinavia, I'll try to draw on another intuition that may feel close to home for people. So We can get some sense of intuition here by thinking about how skiing and ski lifts works. What do I mean by that? So imagine you're wandering through a mountain range, And someone has sort of randomly thrown down ski lifts all over this mountain range. So what you tend to do is, you know, you're sort of Maybe switching skis if you have to.
Jeremy England I'm not much of a skier, so I don't really understand how this works. But probably covering overground, you're gonna use cross country skis, and then when you go downhill, you use downhill skis. In any case, you're not gonna ski uphill. That's really difficult. Or at least, you know and maybe every so often, you'll kind of, like, walk like this up some short hill, but you're not gonna try to scale some big, tall mountain that way.
Jeremy England So what happens as you explore this landscape is that over time, you tend to cross country ski in the directions you can. And every so often, you go over a short hill and then come down the other side. But When you go over a big hill, it's going to be because there's a ski lift that carries you up 1 side, and then you can ski down the other. And I think the important intuition here is it's like this particle where we lift up the energy from the external field, but then when we drop down the other side, we're just losing all that energy into the surroundings. Once you reach the bottom of the hill, you can't just go back up the side of another mountain.
Jeremy England You've lost that energy. You've dissipated it into the surroundings. So now the question is, if this happens for long enough, where do you end up? And my claim would be that in a very large landscape with lots of mountains and lots of randomly thrown down ski lifts, you're gonna end up being driven into directions that it so happens theory are lots of ski lifts that theory you into a particular region of Speaker. And it so happens theory aren't very many that carry you out.
Jeremy England And what that corresponds to is the idea that Each place you are in this mountain range is like a particular arrangement of the atoms of some system. And some arrangements, because they resonate more or some generalization of that. They move more. They're getting more work absorption. So they're like a region where there's a lot of ski lifts as it happens.
Jeremy England And then there are other regions where you don't have so many ski lifts. And in general, you have particular directions that so happens the ski lifts point in. All of this is gonna arise from the specific details of how Atoms or molecules interact in your system. But what it tells you is that over time, doing a seemingly random exploration of this space, You're going to not explore all of it equally. You're gonna end up getting driven or drifting into particular regions of configuration which are the special ones that are particularly good at ski lifting, which are particularly good at absorbing that work from the surrounding environment.
Jeremy England And then you'll kind of get stuck there because you'll ski down some hill, and you won't be able to come back. Now I know that sounds I mean, you wouldn't be stupid enough in reality to ski into a valley if you looked around and you saw there was no way getting out. But remember, we're doing this blind from fluctuation, in fact. We're doing this in a very high dimensional space where the system is just making random moves. So maybe if you were blindfolded in skiing, then you might end up in this little ravine where you could ski down and not get back up.
Jeremy England Alright. So What does this mean for us? Well, I think already what's striking is that what I've laid out before you is highly suggestive, If you're willing to take an intuitive leap with me of some of the organization that we see in biological systems. Because if I look at a plant, I think 1 of the things that I could claim about it is that it is much better at reliably absorbing work energy from the environment that it lives in than most of the ways of randomly rearranging the atoms out of which it's built. There is something special about its organization that we recognize England that is connected to very well defined physical properties that the system has.
Jeremy England So a lot of outcomes of biological organization suddenly Seem to us to be very good examples of systems that have this property that we're now reaching for. We say we have a general tendency towards the discovery of organized states Where the story of how they formed is that they absorbed a lot of work from the environment and somehow caused a lot of dissipation in the surroundings as a result. So that's suggestive, but it doesn't immediately tell us that we understand everything about biological systems. What we're trying to reach for now In my group is just some simple preliminary tests of this idea in much simpler systems. We wanna see if we can test the general intuition of this principle of self organization in systems that we know are definitely not alive, but they do obey Newton's laws and live in a heat bath.
Jeremy England And a student of mine found a paper where, actually, it's already exciting that there's an experimental example that's very suggestive like this. So this was an experiment done where Silver particles were clumping together on the nanoscale while someone was shining light of a certain color on it. And what they found is that the color of the light affected how the rods clump together and that they tended to clump in states that were better at resonating with the applied color of the light field. So You may already have examples and experiment where you see some kind of self organization phenomenon of this sort, but we wanna look for some kind of test of this, in a simulation framework where we can really control the physical parameters, and just see whether the adaptation phenomenon that we're looking for can emerge. So what we did was we defined what I would call a toy chemistry.
Jeremy England We said we have a bunch of particles, and they just live In a fluctuating bath, they they experience a frictional force so they can dissipate a random force so they're contacting a a thermal bath that randomizes the motions. But then they also in addition to obeying Newtonian mechanics in that way, there's a rule that you can make up where you have a simple Arrhenius modification where you add in a rule where there's a forward rate and a reverse rate. And The forward rate and reverse rate are controlled by an Arrhenius like law where you define some activation barrier that's controlled by the distance between the particles. So How does this work? We take the system.
Jeremy England We put it in the thermal bath, so it's gonna fluctuate. The particles are gonna randomly move around Because there are harmonic springs that are allowed to form between the particles according to this rule, the system is also gonna vibrate over time. But then as it vibrates, it can also form and break bonds according to this stochastic random process. So you have An evolving wiring, an evolving network of springs over time. And then what we do is we just take 1 or more of the particles England we apply an external field.
Jeremy England So we wiggle them. We do work on the system, and we allow it to vibrate and fluctuate in a way that will never allow it to reach thermal equilibrium. And instead, These bonds are gonna form and break while there's a possibility of work being done by the external field. So this is now gonna be a movie of what happens in this system where you just take a bunch of particles. And when I mean a bunch, I say I think this is for 30 particles maybe.
Jeremy England And you just allow bonds to form and break, and it's gonna be driven at this frequency. So on the x axis here is frequency. This is the driving frequency. This is the distribution of vibrational frequencies that you see in the system at thermal equilibrium before you start driving the system. And then this is what happens when you start driving the system.
Jeremy England So over time, this network that we have in the system is rewiring itself. Bonds are forming and breaking. And as they do, the spectrum of resonant enter resonant frequencies in the system is altered, and it's pulled towards the driving frequency. And much more interesting than that, I think, is that down here, what we have are the amplitudes of all the different normal modes of the driven system. So What we're basically saying is there are all of these different modes of motion in the system.
Jeremy England And initially, what's plotted on the y axis is How much they respond to being driven at the particular frequency that they're at in the particular driving field the system is experiencing as we drive this 1 particle. England then over time, what you see is that not only this thing this do things pull in the direction of the driving frequency, but you also see much bigger amplitudes. So something about the topology of this whole network is reorganizing so that these modes are soaking up more energy from the applied driving field. And this is happening spontaneously just because things are fluctuating, and evolving according to Newton's laws as they do. So what else we can look at?
Jeremy England This is very new stuff, so we're still puzzling over it and trying to make sense of it. I think this is a simulation for 15 particles. You can't really see the bonds here. I need to make a better graphic of this. We we just generated this a few days before I came England so what what you may be able to make out here is that these particles are colored by the number of bonds that they have.
Jeremy England And so over time, This is how an equilibrium simulation looks where all the colors are fluctuating a lot. And here, you see a convergence on more bonds for the driven particle here And then fewer bonds for a bunch of other particles in the system. So something is different about the topological order and how this network is organized. And this is the new form that's emerging that has these special physical properties. I'm not at all expecting this to necessarily look at look like how living things are organized in any sense, except how we view their physical properties.
Jeremy England But what I think is interesting is we can already establish that these physical properties are connected with the likely emergent order that you see in the system. So particularly, if you track the total entropy production in the surroundings over time For individual trajectories of the system and you plot the frequency spectrum for these individual microtrajectories down here, There's a red trace and a blue trace and a green trace up here, and then there are the corresponding spectra down here. And what you see over time is that for these individual microtrajectories that so happen to do more entropy production, these are also the ones that have moved in the direction of accumulating more resonance. So Becoming organized in a state that happens to be better adapted in a well defined physical sense to the environment corresponds to being a trajectory that causes more entropy production in the surroundings by getting more work done on the system from the, from the driving field. So These are first suggestive observations.
Jeremy England We still have a lot more to do drilling down even just on the system. But I think the outlook is is very exciting from this standpoint because We're starting to see is that maybe we can get the emergence of what might be a well defined sense of physical adaptation in the structure of driven systems where we can really play around with a huge combinatorial space of possible arrangements and be surprised By the organization and structural complexity of the forms that we discover while doing this. So I think that the way that I'll just summarize this, is saying that time reversibility of Newton's laws guarantees a relationship between irreversibility and entropy production. The structures that form through reliable entropy production in a time varying environment look to us like they're well adapted to eating energy from their surroundings. England what we're already starting to be able to see in the simple simulation framework is that you can take something that's obviously dead or inanimate and has nothing to do with being alive, But as long as it is something that obeys Newton's laws in a heat bath and there's an external source of time varying field that you can use to do work, You see an emergent organization that tracks with our expectation in terms of predicting the adapted properties of the system.
Jeremy England And that is the same Method of prediction that looking towards the organization of biological systems is very suggestive in explaining how they work. 1 thing that I suppose I should add on top of this is that it may not be immediately obvious, but The connection here, back to Darwin, is that if you do have self replicating things in your system, 1 of the ways of being really good at reliably dissipating is to have those self replicating things grow really well. So we're not superseding or proposing an alternative to the idea of Darwinian selection. If you have a system where Darwinian selection can happen, then that is a sensible mechanism for explaining the adaptation that emerges. And there's just a sort of physical mirror image to what's going on where you can think about it in terms of this reliable entropy production.
Jeremy England But the exciting suggestion here is that you can see similarly complex adapted forms perhaps emerging in certain contexts where there is no self replicating mechanism that you can use to lean on in explaining the organization that emerges England where the physics might help us to make sense of what's going on in cases where Darwinian selection is not going to necessarily light the way as well. Also, another thing that is hiding below the surface here but that we're very excited about is that I've been talking to you about oscillating drives. Right? Just pick a frequency, and that's all that happens to the system. But as we know, living things are not just living at some driving frequency.
Jeremy England They experience fluctuating environments. And the exciting idea here is that if you have a fluctuating environment, Then part of being good at getting it to do work on you is anticipating it. Because if the environment is about to start pushing you in this direction, England if you're already running in this direction, you can get it to do more work on it on you, rather. So if you have an environment that fluctuates where there are correlations That make it so that things that have happened to you in the past allow you to make a sensible prediction of what is likely to happen in the YouTube. Then 1 of the things you're driven to become, perhaps, is an organized structure that's capable of behaving in ways that seem to predict future outcomes in the environment.
Jeremy England And so we're really interested in in looking for emergent computation, in these driven sessions, and and that's where we wanna take this next. But I think even just looking at resonance is gonna take us some time. So, you know, the the YouTube Looks very exciting to us in terms of what we have not even begun to understand a little bit of YouTube. But we already feel like we're getting least some solid footing in the theoretical intuition for how these far from equilibrium systems should behave in their self organization. And so I'll close just by saying, Make of this what you will, but I, in retrospect, am really stunned by the intuitive success of this very simple suggestion, in in in Norse mythology is that you have, at the beginning, something that's hot and something that's cold, A forage and some cold mountains with some frost or whatever.
Jeremy England And in between them, you have this complex structure that's forming where There's an entropy production process as you move from hot to cold or for a bath at 1 chemical potential to another. And in the middle, you get this emergent organization that has some real subtlety to it in what it seems to be good at. So whether someone just had a really deep insight that they couldn't even fully a long time ago or or whether there's a a chance resemblance in ideas is for you to decide, but I I mentioned it so long as I'm in Stockholm. And with that, I will close by thanking you all for your attention England also, very much so some excellent students who've been working on this In my group, Tal Kathmand from the Technion, Jeremy Owen from Cambridge University, Robert England at MIT. And I have to thank also, and I'm very pleased to Thomas and Virginia Cabot for endowing my