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I don't get it. To me, entropy is not a physical thing, but a measure of our imperfect knowledge about a system. We can only measure the bulk properties of mat

I don't get it. To me, entropy is not a physical thing, but a measure of our imperfect knowledge about a system. We can only measure the bulk properties of matter, so we've made up a number to quantify how imperfect the bulk properties describe the true microscopic state of the system. But if we had the ability to zoom into the microscopic level, entropy would make no sense. So I don't see how gravity or any other fundamental physical interaction could follow from entropy. It's a made-up thing by humans.

bmitc 1y ago
> It's a made-up thing by humans. All of physics is made up by humans.
deleted 1y ago
[deleted]
logicchains 1y ago
Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assumes, as the name implies, that reality at the smallest level can be quantised, so it's completely appropriate to apply entropy to describing things at the microscopic scale.
- kgwgk 1y ago
  > Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. There are no probability distributions over possible states when there is perfect knowledge of the state. > Quantum mechanics Entropy is also zero for a pure quantum state. You won’t have entropy without imperfect knowledge.
  - whereismyacc 1y ago
    > There are no probability distributions over possible states when there is perfect knowledge of the state. I know very little about physics but I thought that the leading interpretations of quantum physics say that the probability distribution is all we can know about a system. The entropy is not due to due to a lack of information about the quantum state, but because the outcomes are inherently stochastic?
    - kgwgk 1y ago
      Entropy is about the state - not about “outcomes”. “All we can know” is the precise state - at least in principle - and entropy is zero in that case.
  - mr_mitm 1y ago
    Just look at the definition of entropy. Knowledge about a system never enters the equation. S := -k_B sum p_i ln (p_i)
    - kgwgk 1y ago
      p_i Edit to add lots of words: In the definition of entropy S := -k_B sum p_i ln (p_i) knowledge about the system enters the equation in the p_i terms. The other term is a constant so it’s not like there are many other choices to link the entropy to the system!
      - mr_mitm 1y ago
        Please communicate in full sentences with me. I can only guess that your objection is something about probabilities. A microstate has a probability independent of my knowledge of the system just like the probability of having a royal flush doesn't change after drawing five cards. The probability of me ending the game with a royal flush might, but that is not what we mean by these probabilities.
        kgwgk 1y ago
        The same microstate will have different probabilities depending on what are the constraints or measurements used in _your_ description of the system. If you choose to describe the system using its microstate - and you know it - there are no probabilities anywhere. You can of course know something and choose to ignore it - the entropy is still a reflection of the uncertainty (actual or for the sake of a lower-resolution model).
        tsimionescu 1y ago
        But the point is that, regardless of how you choose to describe or even measure the system, it will need exactly as much heat to raise its temperature by 1 degree (or it will need as much kinetic energy to increase the average velocity of the constituents by the same amount, in the microstate framework). So there is some objective nature to entropy, it's not merely a function of subjective knowledge of a system. Or, to put it another way, two observers with different amounts of information on the microstate of a system will still measure it as having the same entropy.
- aurareturn 1y ago
  If we knew the exact state of all particles in an enclosed system, we can calculate what future states will be exactly. No need to calculate possible states.
  - IAmBroom 1y ago
    Since that's not possible in any physical system of one or more particles, it's irrelevant.
  - mensetmanusman 1y ago
    Quantum uncertainty actually says no to this. There is an ‘error’ in any propagating probability field.
willvarfar 1y ago
The way we use the word 'entropy' in computer science is different from how its used in physics. Here is a really good explanation in a great talk! https://youtu.be/Kr_S-vXdu_I?si=1uNF2g9OhtlMAS-G&t=2213 https://youtu.be/Kr_S-vXdu_I?si=1uNF2g9OhtlMAS-G&t=2213
antonvs 1y ago
Your perspective is incorrect. Physical entropy governs real physical processes. Simple example: why ice melts in a warm room. More subtle example: why cords get tangled up over time. Our measures of entropy can be seen as a way of summarizing, at a macro level, the state of a system such as that warm room containing ice, or a tangle of cables, but the measure is not the same thing as the phenomenon it describes. Boltzmann's approach to entropy makes the second law pretty intuitive: there are far more ways for a system to be disordered than ordered, so over time it tends towards higher entropy. That’s why ice melts in a warm room.
- refactor_master 1y ago
  I think original post is confused exactly because of “tangled chords” analogies. Something being “messy” in our daily lives can be a bit subjective, so using the same analogies for natural forces may seem a tad counterintuitive actually. Maybe it would be more fitting to say that it just so happens that our human definition of “messy” aligns with entropy, and not that someone decided what messy atoms look like. I’d say a bucket of water is more neat than a bucket of ice, macroscopically.
- HelloNurse 1y ago
  But "disordered" and "ordered" states are just what we define them to be: for example, cords are "tangled" only because we would prefer arrangements of cords with less knots, and knots form because someone didn't handle the cords carefully. Physical processes are "real", but entropy is a figment.
  - dekken_ 1y ago
    I believe you are correct. Entropy is not a physical quantity, it is a measure of how far a system is from equilibrium. Lots of people talk about order/disorder or macro and micro states, not realizing these are things we've invented and aren't physical in nature.
    - kgwgk 1y ago
      > Entropy is not a physical quantity, it is a measure of how far a system is from equilibrium. That’s funny because the original thermodynamic entropy is defined only for systems in equilibrium.
mjburgess 1y ago
Even if we take that view, gravity is still basically a similar case. What we call "gravity" is really an apparent force, that isnt a force at all when seen from a full 4d pov. Imagine sitting outside the whole universe from t=0,t=end and observing one whole block. Then the trajectories of matter, unaffected by any force at all, are those we call gravitational. From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories. Inertia, on this view, is just a kind of hysteresis the matter distribution of the universe has -- ie., a kind of remembered deformation that persists as the universe evolves.
- tsimionescu 1y ago
  > From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories. On the contrary, entropic gravity works pretty well for the Newtonian view of gravity as a force, and not the GR view of gravity as a deformation of space time and analogous to acceleration. Acceleration is a very elementary concept, one you find even in microscopic descriptions. Gravity being essentially the same thing makes it far more elementary than a concept like entropy, which only applies to large groups of particles. So, if the GR picture is the right one, if gravity and acceleration are essentially the same thing, its very hard to see how that aligns with gravity being an emergent phenomenon that only happens at large scales. However, if gravity is just a tendency for massive objects to come together, as in the Newtonian picture, that is perfectly easy to imagine as an entropic effect.
prof-dr-ir 1y ago
Good question. You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0]. Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at: https://en.wikipedia.org/wiki/Entropic_force https://en.wikipedia.org/wiki/Entropic_force and in particular the example that is always used in a first class on this topic: https://en.wikipedia.org/wiki/Ideal_chain https://en.wikipedia.org/wiki/Ideal_chain So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon". Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy. The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law. [0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
- meindnoch 1y ago
  Sure, I'm not denying that entropy exists as a concept, that can be used to explain things macroscopically. But like you said, it's origins are statistical. To me, temperature is also a similar "made up" concept. We can only talk about temperature, because a sufficiently large group of particles will converge to a single-parameter distribution with their velocities. A single particle in isolation doesn't have a temperature. So if they say gravity might be an entropic effect, does that mean that they assume there's something more fundamental "underneath" spacetime that - in the statistical limit - produces the emergent phenomenon of gravity? So it isn't the entropy of matter that they talk about, but the entropy of something else, like the grains of spacetime of whatever.
mjanx123 1y ago
Entropy is the opposite of potential
- echelon 1y ago
  Entropy is complicated beyond just a Rankine or Carnot cycle. Biology thrives at the ebbs, flows, and eddies of entropy. Predation. Biochemical flux. There are arrows flowing every which way, and systems that keep it finely tuned. This theory, based on my surface level reading and understanding, is that the aggregate particle-level entropy within sub light speed systems creates gravity.
whereismyacc 1y ago
It sounds like you're talking about information entropy which to my understanding is analogue to but not the same as entropy in physics?
- ajkjk 1y ago
  It pretty much is the same, except that entropy in physics usually has a constant in front of it.
IsTom 1y ago
If you want to only have one possible past (i.e. can't destroy information) then when you end up in one branch of quantum state you need to "store" enough information to separate you form other branches and you really do need to have multiple possible microstates to differentiate them. If you look post-factum obviously you did end up in a specific state, but statistics do their work otherwise.
sixo 1y ago
This comment thread is exhibit N-thousand that "nobody really understands entropy". My basic understanding goes like this: In thermodynamics, you describe a system with a massive number of microstates/dynamical variable according to 2-3 measurable macrostate variables. (E.g. `N, V, E` for an ideal gas.) If you work out the dynamics of those macrostate variables, you will find that (to first order, i.e. in the thermodynamic limit) they depend only on the form of the entropy function of the system `S(E, N, V)`, e.g. Maxwell relations. If you measured a few more macrostate variables, e.g. the variance in energy `sigma^2(E)` and the center of mass `m`, or anything else, you would be able to write new dynamical relations that depend on a new "entropy" `S(E, N, V, sigma^2(E), m)`. You could add 1000 more variables, or a million—e.g every pixel of an image—basically up until the point where the thermodynamic limit assumptions cease to hold. The `S` function you'd get will capture the contribution of every-variable-you're-marginalizing-over to the relationships between the remaining variables. This is the sense in which it represents "imperfect knowledge". Entropy dependence arises mathematically in the relationships between macrostate variables—they can only couple to each by way of this function which summarizes all the variables you don't know/aren't measuring/aren't specifying. That this works is rather surprising! It depends on some assumptions which I cannot remember (on convexity and factorizeabiltiy and things like that), but which apply to most or maybe all equilibrium thermodynamic-scale systems. For the ideal gas, say, the classical-mechanics, classical-probability, and quantum-mechanic descriptions of the system all reduce to the same `S(N, V, E)` function under this enormous marginalization—the most "zoomed-out" view of their underlying manifold structures turns out to be identical, which is why they all describe the same thing. (It is surprising that seemingly obvious things like the size of the particles would not matter. It turns out that the asymptotic dynamics depend only on the information theory of the available "slots" that energy can go into.) All of this appears as an artifact of the limiting procedure in the thermodynamic limit, but it may be the case that it's more "real" than this—some hard-to-characterize quantum decoherence may lead to this being not only true in an extraordinarily sharp first-order limit, but actually physically true. I haven't kept up with the field. No idea how to apply this to gravity though.
immibis 1y ago
Entropy can be defined as the logarithm of the number of microstates in a macrostate. Since transition between microstates is reversible, and therefore one-to-one (can't converge on any particular microstate, can't go in cycles, have to be something like a random walk) we're more likely to end up in a macrostate that holds a larger number of microstates. For example, there are many more ways your headphone cord can be tangled than untangled, so when you pull it out of your pocket, and it's in a random state, then it's very likely to be tangled. If entropy causes gravity, that means there are more somehow more microstates with all the mass in the universe smooshed together than microstates with all the mass in the universe spread apart.
Ma8ee 1y ago
Entropy is certainly a physical “thing”, in the sense that it affects the development of the system. You can equally well apply your argument that it isn’t a physical thing because it doesn’t exist on a microscopic scale to temperature. Temperature doesn’t exist when you zoom in on single particles either. There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
- kgwgk 1y ago
  > Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us. That number also exists independently of the system! I can imagine any system and calculate the corresponding number. (And for an even more philosophical question, does the “system” really exist independently of us? What separates the “system” from anything else? Is every subset of the universe a “system”?)
- fc417fc802 1y ago
  Exactly! Temperature isn't fundamental. It's a statistical measure made up by humans. It's certainly a very useful abstraction but it isn't a fundamental property. It describes an emergent pattern observed in larger systems. Same for entropy (and also AFAIK angular momentum). It's entirely possible I'm wrong about any of the above but if so I've yet to encounter a convincing line of reasoning.
  - Ma8ee 1y ago
    With the same line of reasoning you can argue (and some have) that numbers aren’t fundamental and are only made up by humans. In my view, the number of swans in the pond is three whether humans exist or not.
    - fc417fc802 1y ago
      I think that's conflating distinct concepts. Numbers aren't a physical property. Whether or not they're a fundamental concept is largely a philosophical question. Meanwhile temperature (for example), while physical, is a statistical property of a macroscopic system. It isn't fundamental - rather it's an abstraction over a (very) large set - but it is nonetheless a quantification of physical characteristics. Whereas a number, for example 2 rocks, is not quantifying any physical property of the individual rocks themselves.
tsoukase 1y ago
For years I thought the same for entropy. But now I believe it is fundamentaly impossible to know each micro state, irrespective our tools and methods. And this happens like and due to Heisenberg's uncertainty principle. So all events are irreversible and entropy is always increasing. Perfection is only theoretical.
analog31 1y ago
Something to consider is that entropy has units of measure. Why would a purely philosophical concept be given units of Joules per Kelvin? I'm only reminded about this because, though I'm a physicist, I've been out of school for more than 3 decades, and decided that I owed myself a refresher on thermodynamics. This coincided with someone on HN recommending David Tong's textbook-quality lecture notes: https://www.damtp.cam.ac.uk/user/tong/statphys.html https://www.damtp.cam.ac.uk/user/tong/statphys.html I think at least the first few pages are readable to a layperson, and address the issue of our imperfect knowledge of the precise configuration of a system containing, say, 1e23 particles. But if we knew all of those relationships, the system would still have entropy.

bmitc 1y ago

> It's a made-up thing by humans. All of physics is made up by humans.

deleted 1y ago

[deleted]

logicchains 1y ago

Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assumes, as the name implies, that reality at the smallest level can be quantised, so it's completely appropriate to apply entropy to describing things at the microscopic scale.

kgwgk 1y ago
> Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. There are no probability distributions over possible states when there is perfect knowledge of the state. > Quantum mechanics Entropy is also zero for a pure quantum state. You won’t have entropy without imperfect knowledge.
- whereismyacc 1y ago
  > There are no probability distributions over possible states when there is perfect knowledge of the state. I know very little about physics but I thought that the leading interpretations of quantum physics say that the probability distribution is all we can know about a system. The entropy is not due to due to a lack of information about the quantum state, but because the outcomes are inherently stochastic?
  - kgwgk 1y ago
    Entropy is about the state - not about “outcomes”. “All we can know” is the precise state - at least in principle - and entropy is zero in that case.
- mr_mitm 1y ago
  Just look at the definition of entropy. Knowledge about a system never enters the equation. S := -k_B sum p_i ln (p_i)
  - kgwgk 1y ago
    p_i Edit to add lots of words: In the definition of entropy S := -k_B sum p_i ln (p_i) knowledge about the system enters the equation in the p_i terms. The other term is a constant so it’s not like there are many other choices to link the entropy to the system!
    - mr_mitm 1y ago
      Please communicate in full sentences with me. I can only guess that your objection is something about probabilities. A microstate has a probability independent of my knowledge of the system just like the probability of having a royal flush doesn't change after drawing five cards. The probability of me ending the game with a royal flush might, but that is not what we mean by these probabilities.
      - kgwgk 1y ago
        The same microstate will have different probabilities depending on what are the constraints or measurements used in _your_ description of the system. If you choose to describe the system using its microstate - and you know it - there are no probabilities anywhere. You can of course know something and choose to ignore it - the entropy is still a reflection of the uncertainty (actual or for the sake of a lower-resolution model).
        tsimionescu 1y ago
        But the point is that, regardless of how you choose to describe or even measure the system, it will need exactly as much heat to raise its temperature by 1 degree (or it will need as much kinetic energy to increase the average velocity of the constituents by the same amount, in the microstate framework). So there is some objective nature to entropy, it's not merely a function of subjective knowledge of a system. Or, to put it another way, two observers with different amounts of information on the microstate of a system will still measure it as having the same entropy.
aurareturn 1y ago
If we knew the exact state of all particles in an enclosed system, we can calculate what future states will be exactly. No need to calculate possible states.
- IAmBroom 1y ago
  Since that's not possible in any physical system of one or more particles, it's irrelevant.
- mensetmanusman 1y ago
  Quantum uncertainty actually says no to this. There is an ‘error’ in any propagating probability field.

willvarfar 1y ago

The way we use the word 'entropy' in computer science is different from how its used in physics. Here is a really good explanation in a great talk! https://youtu.be/Kr_S-vXdu_I?si=1uNF2g9OhtlMAS-G&t=2213 https://youtu.be/Kr_S-vXdu_I?si=1uNF2g9OhtlMAS-G&t=2213

antonvs 1y ago

Your perspective is incorrect. Physical entropy governs real physical processes. Simple example: why ice melts in a warm room. More subtle example: why cords get tangled up over time. Our measures of entropy can be seen as a way of summarizing, at a macro level, the state of a system such as that warm room containing ice, or a tangle of cables, but the measure is not the same thing as the phenomenon it describes. Boltzmann's approach to entropy makes the second law pretty intuitive: there are far more ways for a system to be disordered than ordered, so over time it tends towards higher entropy. That’s why ice melts in a warm room.

refactor_master 1y ago
I think original post is confused exactly because of “tangled chords” analogies. Something being “messy” in our daily lives can be a bit subjective, so using the same analogies for natural forces may seem a tad counterintuitive actually. Maybe it would be more fitting to say that it just so happens that our human definition of “messy” aligns with entropy, and not that someone decided what messy atoms look like. I’d say a bucket of water is more neat than a bucket of ice, macroscopically.
HelloNurse 1y ago
But "disordered" and "ordered" states are just what we define them to be: for example, cords are "tangled" only because we would prefer arrangements of cords with less knots, and knots form because someone didn't handle the cords carefully. Physical processes are "real", but entropy is a figment.
- dekken_ 1y ago
  I believe you are correct. Entropy is not a physical quantity, it is a measure of how far a system is from equilibrium. Lots of people talk about order/disorder or macro and micro states, not realizing these are things we've invented and aren't physical in nature.
  - kgwgk 1y ago
    > Entropy is not a physical quantity, it is a measure of how far a system is from equilibrium. That’s funny because the original thermodynamic entropy is defined only for systems in equilibrium.

mjburgess 1y ago

Even if we take that view, gravity is still basically a similar case. What we call "gravity" is really an apparent force, that isnt a force at all when seen from a full 4d pov. Imagine sitting outside the whole universe from t=0,t=end and observing one whole block. Then the trajectories of matter, unaffected by any force at all, are those we call gravitational. From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories. Inertia, on this view, is just a kind of hysteresis the matter distribution of the universe has -- ie., a kind of remembered deformation that persists as the universe evolves.

tsimionescu 1y ago
> From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories. On the contrary, entropic gravity works pretty well for the Newtonian view of gravity as a force, and not the GR view of gravity as a deformation of space time and analogous to acceleration. Acceleration is a very elementary concept, one you find even in microscopic descriptions. Gravity being essentially the same thing makes it far more elementary than a concept like entropy, which only applies to large groups of particles. So, if the GR picture is the right one, if gravity and acceleration are essentially the same thing, its very hard to see how that aligns with gravity being an emergent phenomenon that only happens at large scales. However, if gravity is just a tendency for massive objects to come together, as in the Newtonian picture, that is perfectly easy to imagine as an entropic effect.

prof-dr-ir 1y ago

Good question. You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0]. Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at: https://en.wikipedia.org/wiki/Entropic_force https://en.wikipedia.org/wiki/Entropic_force and in particular the example that is always used in a first class on this topic: https://en.wikipedia.org/wiki/Ideal_chain https://en.wikipedia.org/wiki/Ideal_chain So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon". Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy. The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law. [0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.

meindnoch 1y ago
Sure, I'm not denying that entropy exists as a concept, that can be used to explain things macroscopically. But like you said, it's origins are statistical. To me, temperature is also a similar "made up" concept. We can only talk about temperature, because a sufficiently large group of particles will converge to a single-parameter distribution with their velocities. A single particle in isolation doesn't have a temperature. So if they say gravity might be an entropic effect, does that mean that they assume there's something more fundamental "underneath" spacetime that - in the statistical limit - produces the emergent phenomenon of gravity? So it isn't the entropy of matter that they talk about, but the entropy of something else, like the grains of spacetime of whatever.

mjanx123 1y ago

Entropy is the opposite of potential

echelon 1y ago
Entropy is complicated beyond just a Rankine or Carnot cycle. Biology thrives at the ebbs, flows, and eddies of entropy. Predation. Biochemical flux. There are arrows flowing every which way, and systems that keep it finely tuned. This theory, based on my surface level reading and understanding, is that the aggregate particle-level entropy within sub light speed systems creates gravity.

whereismyacc 1y ago

It sounds like you're talking about information entropy which to my understanding is analogue to but not the same as entropy in physics?

ajkjk 1y ago
It pretty much is the same, except that entropy in physics usually has a constant in front of it.

IsTom 1y ago

If you want to only have one possible past (i.e. can't destroy information) then when you end up in one branch of quantum state you need to "store" enough information to separate you form other branches and you really do need to have multiple possible microstates to differentiate them. If you look post-factum obviously you did end up in a specific state, but statistics do their work otherwise.

sixo 1y ago

This comment thread is exhibit N-thousand that "nobody really understands entropy". My basic understanding goes like this: In thermodynamics, you describe a system with a massive number of microstates/dynamical variable according to 2-3 measurable macrostate variables. (E.g. `N, V, E` for an ideal gas.) If you work out the dynamics of those macrostate variables, you will find that (to first order, i.e. in the thermodynamic limit) they depend only on the form of the entropy function of the system `S(E, N, V)`, e.g. Maxwell relations. If you measured a few more macrostate variables, e.g. the variance in energy `sigma^2(E)` and the center of mass `m`, or anything else, you would be able to write new dynamical relations that depend on a new "entropy" `S(E, N, V, sigma^2(E), m)`. You could add 1000 more variables, or a million—e.g every pixel of an image—basically up until the point where the thermodynamic limit assumptions cease to hold. The `S` function you'd get will capture the contribution of every-variable-you're-marginalizing-over to the relationships between the remaining variables. This is the sense in which it represents "imperfect knowledge". Entropy dependence arises mathematically in the relationships between macrostate variables—they can only couple to each by way of this function which summarizes all the variables you don't know/aren't measuring/aren't specifying. That this works is rather surprising! It depends on some assumptions which I cannot remember (on convexity and factorizeabiltiy and things like that), but which apply to most or maybe all equilibrium thermodynamic-scale systems. For the ideal gas, say, the classical-mechanics, classical-probability, and quantum-mechanic descriptions of the system all reduce to the same `S(N, V, E)` function under this enormous marginalization—the most "zoomed-out" view of their underlying manifold structures turns out to be identical, which is why they all describe the same thing. (It is surprising that seemingly obvious things like the size of the particles would not matter. It turns out that the asymptotic dynamics depend only on the information theory of the available "slots" that energy can go into.) All of this appears as an artifact of the limiting procedure in the thermodynamic limit, but it may be the case that it's more "real" than this—some hard-to-characterize quantum decoherence may lead to this being not only true in an extraordinarily sharp first-order limit, but actually physically true. I haven't kept up with the field. No idea how to apply this to gravity though.

immibis 1y ago

Entropy can be defined as the logarithm of the number of microstates in a macrostate. Since transition between microstates is reversible, and therefore one-to-one (can't converge on any particular microstate, can't go in cycles, have to be something like a random walk) we're more likely to end up in a macrostate that holds a larger number of microstates. For example, there are many more ways your headphone cord can be tangled than untangled, so when you pull it out of your pocket, and it's in a random state, then it's very likely to be tangled. If entropy causes gravity, that means there are more somehow more microstates with all the mass in the universe smooshed together than microstates with all the mass in the universe spread apart.

Ma8ee 1y ago

Entropy is certainly a physical “thing”, in the sense that it affects the development of the system. You can equally well apply your argument that it isn’t a physical thing because it doesn’t exist on a microscopic scale to temperature. Temperature doesn’t exist when you zoom in on single particles either. There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.

kgwgk 1y ago
> Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us. That number also exists independently of the system! I can imagine any system and calculate the corresponding number. (And for an even more philosophical question, does the “system” really exist independently of us? What separates the “system” from anything else? Is every subset of the universe a “system”?)
fc417fc802 1y ago
Exactly! Temperature isn't fundamental. It's a statistical measure made up by humans. It's certainly a very useful abstraction but it isn't a fundamental property. It describes an emergent pattern observed in larger systems. Same for entropy (and also AFAIK angular momentum). It's entirely possible I'm wrong about any of the above but if so I've yet to encounter a convincing line of reasoning.
- Ma8ee 1y ago
  With the same line of reasoning you can argue (and some have) that numbers aren’t fundamental and are only made up by humans. In my view, the number of swans in the pond is three whether humans exist or not.
  - fc417fc802 1y ago
    I think that's conflating distinct concepts. Numbers aren't a physical property. Whether or not they're a fundamental concept is largely a philosophical question. Meanwhile temperature (for example), while physical, is a statistical property of a macroscopic system. It isn't fundamental - rather it's an abstraction over a (very) large set - but it is nonetheless a quantification of physical characteristics. Whereas a number, for example 2 rocks, is not quantifying any physical property of the individual rocks themselves.

tsoukase 1y ago

For years I thought the same for entropy. But now I believe it is fundamentaly impossible to know each micro state, irrespective our tools and methods. And this happens like and due to Heisenberg's uncertainty principle. So all events are irreversible and entropy is always increasing. Perfection is only theoretical.

analog31 1y ago

Something to consider is that entropy has units of measure. Why would a purely philosophical concept be given units of Joules per Kelvin? I'm only reminded about this because, though I'm a physicist, I've been out of school for more than 3 decades, and decided that I owed myself a refresher on thermodynamics. This coincided with someone on HN recommending David Tong's textbook-quality lecture notes: https://www.damtp.cam.ac.uk/user/tong/statphys.html https://www.damtp.cam.ac.uk/user/tong/statphys.html I think at least the first few pages are readable to a layperson, and address the issue of our imperfect knowledge of the precise configuration of a system containing, say, 1e23 particles. But if we knew all of those relationships, the system would still have entropy.