17 ms·

> But if you look deeper than that averaging it stops making sense to me. It's a completely different world. I think you're less confused than you think you ar

> But if you look deeper than that averaging it stops making sense to me. It's a completely different world. I think you're less confused than you think you are! As I posted elsewhere, it helps to think of entropy as a quantity that actually depends on how much you know about the system in question. Typically when you calculate the entropy of a system at temperature X, that means all you know is that you stuck a thermometer in it and measured X. You don't know anything more than the average temperature. It could be in any state consistent with that temperature. If you know more about the system, it has less entropy. If you know it down to the exact microstate, it has zero entropy.

andi999 4y ago
Entropy (differences) are an objective quantity which can be measured, there is no subjectivity about it. It is not which parameters you know it is about which parameters you hold fixed.
- oldsecondhand 4y ago
  I think he is confusing the usage of entropy in physics and computer science. In computer science entropy is conditional probability and depends on what we know about a system.
  - kgwgk 4y ago
    As it does in physics! "which parameters [thermodynamic variables] you know" ~ "which parameters [thermodynamic variables] you hold fixed" (or know in average, like the energy for a system in a heat bath where the temperature is fixed) https://bayes.wustl.edu/etj/articles/theory.1.pdf https://bayes.wustl.edu/etj/articles/theory.1.pdf http://nicf.net/articles/thermodynamics-statistical-mechanics/ http://nicf.net/articles/thermodynamics-statistical-mechanic...
    - oldsecondhand 4y ago
      You can observe the movement of molecules beyond macro properties like temperature.
      - kgwgk 4y ago
        Sure, at least in principle. And if you knew what every molecule was doing the entropy would vanish.
        IX-103 4y ago
        I've thought that for a while, but I'm not a physicist. Do you know any prominent physicists that hold that view? It seems to contradict at least the popular narrative about entropy as a property of a system.
        kgwgk 4y ago
        > Do you know any prominent physicists that hold that view? The view that the entropy of a microstate (i.e. a perfectly defined physical state) is zero? All of them, hopefully.
        liminvorous 4y ago
        I only have an undergraduate degree in physics, but I think the point you may be missing is that information requires some physical medium to store it. So entropy is very roughly speaking the property of the system that determines how big a hard drive you need to store a description of that system.
- toxik 4y ago
  Leonard Susskind disagrees with you. See his lectures on statistical mechanics, he is very clear that entropy is a matter of knowledge about the system. It has to be.
  - oh_my_goodness 4y ago
    Susskind says that entropy is determined by selecting a macro-state. He doesn't claim that the entropy of a macro-state depends on whether we know which macro-state the real system is really in. If we happen to know, then, sure. For example we could pick a weird-ass observable state, and when we saw it we would know the entropy of the system was low. But the entropy of each macro-state just depends on how many micro-states we define it to contain. It doesn't depend on our knowledge of the system state.
    - jbay808 4y ago
      The concept of entropy wasn't invented so that we could calculate entropies of macrostates, it was so that we could calculate entropies of real systems and understand their behaviour. Macrostates are an accounting tool that helps us do this. You seem to be treating the calculation of macrostate entropy as an end-goal in itself, but also allowing yourself to somehow freely choose any macrostate you want. When it comes to applying thermodynamics in practice, you'll have to calculate the entropy of a real, or at least hypothetical, system. The point of macrostates is that you ought to know which macrostate a given system is in. That's the thing that you know. You don't know which microstate it's in, but you do know which macrostate it's in. For example, if I say "a cubic metre volume of air at room temperature and pressure", I've described a physical system. I've also described a macrostate. If you're calculating the entropy of macrostates that are not consistent with a description of a system -- if you've defined your macrostates such that you don't know which macrostate a given system is in -- then in order to calculate that system's entropy you have to sum up over all such possible macrostates anyway, so you haven't saved yourself any work or earned any insights along the way. So yes, you can calculate the entropy of a macrostate without knowing what macrostate a real system is in, but it kind of sounds like you're arguing that log(x) is not a function of variable x, because log(3) is a constant and log(4) is a constant, and you can divide up any x into constants of your choice.
- jbay808 4y ago
  No, it is subjective. We just only have such blunt instruments for practically measuring states, relative to the gargantuan amount of entropy in most real systems, that the subjective nature of entropy is easy to miss. But in a world where the frontiers of thermodynamics have moved from steam engines to lasers, computers, DNA, and black holes, the difference is increasingly obvious and important. With steam engines, we got away with treating a volume of gas as having not only a few parameters that we knew and cared about, like mass, temperature and pressure, but we could further deceive ourselves into thinking that those were the only parameters that existed to describe the system. The only parameters that were knowable. But Boltzmann knew better. Look at Boltzmann's formula, S = kB log W. For any single particular system you describe to me, W will be 1, and so S will be 0. So it's only if you describe an ensemble of systems -- that is, if you describe a system vaguely, such that I am left to imagine the details -- that we have nonzero entropy. If you ask me to calculate the entropy of that "system", that macrostate, that ensemble, then sure, I'll end up with nonzero entropy. But if I ask you to keep transmitting more data about the scenario, then with each further description, you'll be narrowing the state space and thereby decreasing the entropy. Look, since the entropy of a macrostate is nonzero, but the entropy of any single microstate which is consistent with that macrostate is zero, it's clear that entropy is not an intrinsic property of any real system. It's a property of how many other possible non-existent systems could be swapped out for the one in front of you, without you noticing the change. If I swap out the air in your room for an equal volume of air at equal temperature and pressure, you probably won't notice. If I swap out the hard drive in your laptop for an equal volume of hard drive at equal temperature and pressure, you probably will!
  - deltaonefour 4y ago
    Very few people know this but. Information entropy and statistical mechanical entropy are two different things. They share the same equation and the same name but they are two unrelated concepts. You have conflated the two. The person you are responding to is referring to statistical entropy. Basically in this entire thread nobody, including you, is fully grasping the situation.
    - jbay808 4y ago
- im3w1l 4y ago
  I've been trying to reconcile these perspectives, and I think it really is both. And they are both physically relevant. Consider the subjective entropy perspective. If you know the exact microstate of a system, then you can in theory play the part of Maxwell's demon. You could have a little gate that you open only for fast particles, and using your knowledge of the microstate, you can predict exactly when they will arrive. But consider the objective perspective. If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process. I haven't fully wrapped my head around it yet, but I do think that acknowledging both is a step in the right direction at least.
  - jbay808 4y ago
    > If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process. The subjective view handles this scenario just fine, though, and makes more accurate predictions than the objective view. For example, there are systems where some aspects of the original microstate survive thermal contact with another system. We use such systems to store data! I bet your hard drive is in thermal contact with its environment right now! It's very hard to reconcile this with an objective take on entropy. And there are some systems that will rapidly be scrambled. The subjective perspective has no problem admitting that your knowledge of a system can become inaccurate and useless. Even without thermal contact, you'd need to perform a tremendous amount of (perhaps reversible) computation in order to make a functioning Maxwell's demon with your initial microstate conditions, because the microstate will evolve in time in a complicated way. The subjective view is still totally consistent with entropy of a system increasing over time!
    - deleted 4y ago
      [deleted]
    - deleted 4y ago
      [deleted]
    - 4y ago
- jwarden 4y ago
  Fascinating discussion. I see some parallel here to the Bayesian vs Frequentist view of probability. They are perhaps both valid points of view depending on the situation. If you take a frequentist view of an unbiased coin, then the probability that it will land heads on the next flip is objectively, by definition 50%. So the resulting calculation of entropy (log 50% = 1 bit) is also objectively defined. But if your 50% probability represents a subjective belief, the resulting entropy calculation should also be considered subjective, I would think.
- alecst 4y ago
  U, the internal energy is objective. The free energy F = U - TS is the maximum amount of work you can extract from the system. This depends on how much you know about the system. S does indeed depend on what you know about the system. See the Gibbs Paradox for more information.
  - mannykannot 4y ago
    If two people disagree on the maximum amount of work that could be extracted from a given system (with both of them basing their figure on their own evaluation of S), are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? If only changes in S (and F) have measurable consequences, would that not merely mean that assigning an absolute value is an arbitrary choice, which would not mean the same as it being subjective (there could still be an objective conversion between one basis and another, as there is for kinetic energy in different inertial reference frames.) In the Gibbs Paradox, there is no subjectivity in whether the gases being mixed are the same or different, and no subjectivity in what the change of entropy is in either case. The paradox is that it does not feel right that identity makes an objective difference between the two cases, but the empirically-demonstrable distinction between fermions and bosons shows that this intuition does not hold in general. I believe Von Neumann came up with a QM resolution of the paradox.
    - jbay808 4y ago
      > are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? Isn't it more interesting to examine a situation where it would be possible to empirically demonstrate that the proponent of the lower figure was wrong?
      - mannykannot 4y ago
        In that case we could objectively say that one value of S does not yield F for that system (given that F is defined as a maximum), but this would not resolve the general question of subjectivity.
vishnugupta 4y ago
This is how I have come to understand entropy. The words disorder and order are a proxy for information content. > If you know more about the system, it has less entropy. One question though. When you say "it" does it include you as well as the system or just the system? To me "it" includes both because by it is "you" who's state has changed by acquiring more information. It could be in the form of neuronal rearrangement or bits being stored in some digital media etc., A new information content has thus been created. There's an interesting side effect if one thinks deep enough here. The system will keep changing its state so the information one is out of date thus leading to more disorder (i.e., information loss) and increased entropy. One can keep the information updated but it takes energy. And I read somewhere that the energy thus used will lead to increase in overall entropy of the universe and thus the 2nd law.
- oh_my_goodness 4y ago
  >This is how I have come to understand entropy. The words disorder and order are a proxy for information content Does information content mean this? ... "How many bits of random-number generator would I need to make the number of micro-states in the macro-state?"
  - vishnugupta 4y ago
    That is my mental model, yes. More bits are needed to capture more detailed (or micro-states as you called it elsewhere in this thread, or finer-grained) information. Let's say there's a stone, we want to know its details. If all we want to know is whether it weighs more than 100KG or not then one bit will do. 1 means > 100KG and 0 means < 100KG. If we want to know its colour (as one of 7 WIBGYOR) as well then we need 4 bits; 3 bits to encode 7 colours and 1 bit to encode yes/no for the weight. And so on..as we gain more and more information we need more bits to store that. This is just for the storage though; in order to gain the information we need to expend energy. More information requires more energy leading to more disorder as expending energy releases heat and thus 2nd order of thermodynamics as well as arrow of time. IMO our perception of time is purely based on memory which is information content of event stored in Neurons. Quite a bit of hand-wavy. But this is a mental model I've developed over the years of thinking and reading (and listening to lectures) about entropy, information, arrow of time, and energy and how they are interconnected.
oh_my_goodness 4y ago
I think that works ok. But I think it's an unnecessarily tricky explanation. Entropy per macro-state decreases as we look at finer-grained macro-states. It feels simpler to associate the entropy of each macro-state with that macro-state, rather than assuming we know which macro-state the system is in, and then attributing the lower entropy to our knowledge of the macro-state. I think it can probably be expressed either way. I just think the "knowledge" part is tricky and can be left out.
- jbay808 4y ago
  Can you elaborate on the difference between a "fine-grained" macrostate and a macrostate that is not fine-grained? I think you will find it hard to separate the concept of a macrostate from the state of knowledge (or ignorance) of an individual subjective observer.
  - oh_my_goodness 4y ago
    Sure. A fine-grained macro-state contains fewer micro-states. A coarse-grained macro-state contains more micro-states. Say I flip 8 coins and I don't look at the results. A fine-grained macro state is TTTT TTTT. A coarser-grained macro state is TTTT xxxx. The one has 4 bits more entropy than the other. It works the same way in statistical mechanics. Call them spins. We're just talking about some ensemble of micro states, and then we divide the ensemble up into macro-states. To do statistical mechanics at all, I think I have to define some macro-states according to which micro-states they contain. That doesn't mean I necessarily have any information about which macro-state the system is actually in.
    - kgwgk 4y ago
      How is a macrostate TTTTxxxx different from having the information about the TTTT part and not about the xxxx part? Talking bout the entropy of the macrostate TTTTxxxx makes sense only conditional on the TTTT information.
      - oh_my_goodness 4y ago
gota 4y ago
Oh my god, this explanation is gold. Thank you. I'm going to save it and refer to it in the future.
deltaonefour 4y ago
No this is completely and utterly wrong. Entropy is not a function of knowledge. Two people with varying and different levels of knowledge of a system does not mean the system has two different entropy values. Even if I knew the exact position of all atoms in a cup of water, the temperature of that water does not change due to that knowledge. Entropy does rely on what your picked configuration of macro states and microstates. Temperature is an arbitrary choice of macrostate.
- jbay808 4y ago
  > Even if I knew the exact position of all atoms in a cup of water, the temperature of that water does not change due to that knowledge. It actually does! You would disagree with the other person about the temperature of that water. But I agree that this is admittedly not obvious at first.
  - deltaonefour 4y ago
    No it does not. The thermometer does not change based off of my knowledge or opinion.
    - jbay808 4y ago
      A thermometer doesn't measure temperature any better than a meterstick measures length. And we all know what Einstein had to say about the relativity of metersticks. To paraphrase from the paper I linked in another reply to you, a thermometer is just a heat bath equipped with a pointer which reads its average energy, whose scale is calibrated to give the temperature T, defined by 1/T = dS/d<E>. You can read the thermometer if you like, but if you know the exact microstate of the water to begin with, the thermometer reading will tell you much less than you already knew about the water. And precise knowledge of the water's microstate will (theoretically) allow you to extract much more work from that water than you would be able to with only the thermometer reading.
      - deltaonefour 4y ago

andi999 4y ago

Entropy (differences) are an objective quantity which can be measured, there is no subjectivity about it. It is not which parameters you know it is about which parameters you hold fixed.

oldsecondhand 4y ago
I think he is confusing the usage of entropy in physics and computer science. In computer science entropy is conditional probability and depends on what we know about a system.
- kgwgk 4y ago
  As it does in physics! "which parameters [thermodynamic variables] you know" ~ "which parameters [thermodynamic variables] you hold fixed" (or know in average, like the energy for a system in a heat bath where the temperature is fixed) https://bayes.wustl.edu/etj/articles/theory.1.pdf https://bayes.wustl.edu/etj/articles/theory.1.pdf http://nicf.net/articles/thermodynamics-statistical-mechanics/ http://nicf.net/articles/thermodynamics-statistical-mechanic...
  - oldsecondhand 4y ago
    You can observe the movement of molecules beyond macro properties like temperature.
    - kgwgk 4y ago
      Sure, at least in principle. And if you knew what every molecule was doing the entropy would vanish.
      - IX-103 4y ago
        I've thought that for a while, but I'm not a physicist. Do you know any prominent physicists that hold that view? It seems to contradict at least the popular narrative about entropy as a property of a system.
        kgwgk 4y ago
        > Do you know any prominent physicists that hold that view? The view that the entropy of a microstate (i.e. a perfectly defined physical state) is zero? All of them, hopefully.
        liminvorous 4y ago
        I only have an undergraduate degree in physics, but I think the point you may be missing is that information requires some physical medium to store it. So entropy is very roughly speaking the property of the system that determines how big a hard drive you need to store a description of that system.
toxik 4y ago
Leonard Susskind disagrees with you. See his lectures on statistical mechanics, he is very clear that entropy is a matter of knowledge about the system. It has to be.
- oh_my_goodness 4y ago
  Susskind says that entropy is determined by selecting a macro-state. He doesn't claim that the entropy of a macro-state depends on whether we know which macro-state the real system is really in. If we happen to know, then, sure. For example we could pick a weird-ass observable state, and when we saw it we would know the entropy of the system was low. But the entropy of each macro-state just depends on how many micro-states we define it to contain. It doesn't depend on our knowledge of the system state.
  - jbay808 4y ago
    The concept of entropy wasn't invented so that we could calculate entropies of macrostates, it was so that we could calculate entropies of real systems and understand their behaviour. Macrostates are an accounting tool that helps us do this. You seem to be treating the calculation of macrostate entropy as an end-goal in itself, but also allowing yourself to somehow freely choose any macrostate you want. When it comes to applying thermodynamics in practice, you'll have to calculate the entropy of a real, or at least hypothetical, system. The point of macrostates is that you ought to know which macrostate a given system is in. That's the thing that you know. You don't know which microstate it's in, but you do know which macrostate it's in. For example, if I say "a cubic metre volume of air at room temperature and pressure", I've described a physical system. I've also described a macrostate. If you're calculating the entropy of macrostates that are not consistent with a description of a system -- if you've defined your macrostates such that you don't know which macrostate a given system is in -- then in order to calculate that system's entropy you have to sum up over all such possible macrostates anyway, so you haven't saved yourself any work or earned any insights along the way. So yes, you can calculate the entropy of a macrostate without knowing what macrostate a real system is in, but it kind of sounds like you're arguing that log(x) is not a function of variable x, because log(3) is a constant and log(4) is a constant, and you can divide up any x into constants of your choice.
jbay808 4y ago
No, it is subjective. We just only have such blunt instruments for practically measuring states, relative to the gargantuan amount of entropy in most real systems, that the subjective nature of entropy is easy to miss. But in a world where the frontiers of thermodynamics have moved from steam engines to lasers, computers, DNA, and black holes, the difference is increasingly obvious and important. With steam engines, we got away with treating a volume of gas as having not only a few parameters that we knew and cared about, like mass, temperature and pressure, but we could further deceive ourselves into thinking that those were the only parameters that existed to describe the system. The only parameters that were knowable. But Boltzmann knew better. Look at Boltzmann's formula, S = kB log W. For any single particular system you describe to me, W will be 1, and so S will be 0. So it's only if you describe an ensemble of systems -- that is, if you describe a system vaguely, such that I am left to imagine the details -- that we have nonzero entropy. If you ask me to calculate the entropy of that "system", that macrostate, that ensemble, then sure, I'll end up with nonzero entropy. But if I ask you to keep transmitting more data about the scenario, then with each further description, you'll be narrowing the state space and thereby decreasing the entropy. Look, since the entropy of a macrostate is nonzero, but the entropy of any single microstate which is consistent with that macrostate is zero, it's clear that entropy is not an intrinsic property of any real system. It's a property of how many other possible non-existent systems could be swapped out for the one in front of you, without you noticing the change. If I swap out the air in your room for an equal volume of air at equal temperature and pressure, you probably won't notice. If I swap out the hard drive in your laptop for an equal volume of hard drive at equal temperature and pressure, you probably will!
- deltaonefour 4y ago
  Very few people know this but. Information entropy and statistical mechanical entropy are two different things. They share the same equation and the same name but they are two unrelated concepts. You have conflated the two. The person you are responding to is referring to statistical entropy. Basically in this entire thread nobody, including you, is fully grasping the situation.
  - jbay808 4y ago
im3w1l 4y ago
I've been trying to reconcile these perspectives, and I think it really is both. And they are both physically relevant. Consider the subjective entropy perspective. If you know the exact microstate of a system, then you can in theory play the part of Maxwell's demon. You could have a little gate that you open only for fast particles, and using your knowledge of the microstate, you can predict exactly when they will arrive. But consider the objective perspective. If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process. I haven't fully wrapped my head around it yet, but I do think that acknowledging both is a step in the right direction at least.
- jbay808 4y ago
  > If you take this very same system and put it in thermal contact with another system, then an objective entropy perspective is the relevant one. Those systems will equilibrize and your subjective knowledge is irrelevant to that process. The subjective view handles this scenario just fine, though, and makes more accurate predictions than the objective view. For example, there are systems where some aspects of the original microstate survive thermal contact with another system. We use such systems to store data! I bet your hard drive is in thermal contact with its environment right now! It's very hard to reconcile this with an objective take on entropy. And there are some systems that will rapidly be scrambled. The subjective perspective has no problem admitting that your knowledge of a system can become inaccurate and useless. Even without thermal contact, you'd need to perform a tremendous amount of (perhaps reversible) computation in order to make a functioning Maxwell's demon with your initial microstate conditions, because the microstate will evolve in time in a complicated way. The subjective view is still totally consistent with entropy of a system increasing over time!
  - deleted 4y ago
    [deleted]
  - deleted 4y ago
    [deleted]
  - 4y ago
jwarden 4y ago
Fascinating discussion. I see some parallel here to the Bayesian vs Frequentist view of probability. They are perhaps both valid points of view depending on the situation. If you take a frequentist view of an unbiased coin, then the probability that it will land heads on the next flip is objectively, by definition 50%. So the resulting calculation of entropy (log 50% = 1 bit) is also objectively defined. But if your 50% probability represents a subjective belief, the resulting entropy calculation should also be considered subjective, I would think.
alecst 4y ago
U, the internal energy is objective. The free energy F = U - TS is the maximum amount of work you can extract from the system. This depends on how much you know about the system. S does indeed depend on what you know about the system. See the Gibbs Paradox for more information.
- mannykannot 4y ago
  If two people disagree on the maximum amount of work that could be extracted from a given system (with both of them basing their figure on their own evaluation of S), are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? If only changes in S (and F) have measurable consequences, would that not merely mean that assigning an absolute value is an arbitrary choice, which would not mean the same as it being subjective (there could still be an objective conversion between one basis and another, as there is for kinetic energy in different inertial reference frames.) In the Gibbs Paradox, there is no subjectivity in whether the gases being mixed are the same or different, and no subjectivity in what the change of entropy is in either case. The paradox is that it does not feel right that identity makes an objective difference between the two cases, but the empirically-demonstrable distinction between fermions and bosons shows that this intuition does not hold in general. I believe Von Neumann came up with a QM resolution of the paradox.
  - jbay808 4y ago
    > are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? Isn't it more interesting to examine a situation where it would be possible to empirically demonstrate that the proponent of the lower figure was wrong?
    - mannykannot 4y ago
      In that case we could objectively say that one value of S does not yield F for that system (given that F is defined as a maximum), but this would not resolve the general question of subjectivity.

vishnugupta 4y ago

This is how I have come to understand entropy. The words disorder and order are a proxy for information content. > If you know more about the system, it has less entropy. One question though. When you say "it" does it include you as well as the system or just the system? To me "it" includes both because by it is "you" who's state has changed by acquiring more information. It could be in the form of neuronal rearrangement or bits being stored in some digital media etc., A new information content has thus been created. There's an interesting side effect if one thinks deep enough here. The system will keep changing its state so the information one is out of date thus leading to more disorder (i.e., information loss) and increased entropy. One can keep the information updated but it takes energy. And I read somewhere that the energy thus used will lead to increase in overall entropy of the universe and thus the 2nd law.

oh_my_goodness 4y ago
>This is how I have come to understand entropy. The words disorder and order are a proxy for information content Does information content mean this? ... "How many bits of random-number generator would I need to make the number of micro-states in the macro-state?"
- vishnugupta 4y ago
  That is my mental model, yes. More bits are needed to capture more detailed (or micro-states as you called it elsewhere in this thread, or finer-grained) information. Let's say there's a stone, we want to know its details. If all we want to know is whether it weighs more than 100KG or not then one bit will do. 1 means > 100KG and 0 means < 100KG. If we want to know its colour (as one of 7 WIBGYOR) as well then we need 4 bits; 3 bits to encode 7 colours and 1 bit to encode yes/no for the weight. And so on..as we gain more and more information we need more bits to store that. This is just for the storage though; in order to gain the information we need to expend energy. More information requires more energy leading to more disorder as expending energy releases heat and thus 2nd order of thermodynamics as well as arrow of time. IMO our perception of time is purely based on memory which is information content of event stored in Neurons. Quite a bit of hand-wavy. But this is a mental model I've developed over the years of thinking and reading (and listening to lectures) about entropy, information, arrow of time, and energy and how they are interconnected.

oh_my_goodness 4y ago

I think that works ok. But I think it's an unnecessarily tricky explanation. Entropy per macro-state decreases as we look at finer-grained macro-states. It feels simpler to associate the entropy of each macro-state with that macro-state, rather than assuming we know which macro-state the system is in, and then attributing the lower entropy to our knowledge of the macro-state. I think it can probably be expressed either way. I just think the "knowledge" part is tricky and can be left out.

jbay808 4y ago
Can you elaborate on the difference between a "fine-grained" macrostate and a macrostate that is not fine-grained? I think you will find it hard to separate the concept of a macrostate from the state of knowledge (or ignorance) of an individual subjective observer.
- oh_my_goodness 4y ago
  Sure. A fine-grained macro-state contains fewer micro-states. A coarse-grained macro-state contains more micro-states. Say I flip 8 coins and I don't look at the results. A fine-grained macro state is TTTT TTTT. A coarser-grained macro state is TTTT xxxx. The one has 4 bits more entropy than the other. It works the same way in statistical mechanics. Call them spins. We're just talking about some ensemble of micro states, and then we divide the ensemble up into macro-states. To do statistical mechanics at all, I think I have to define some macro-states according to which micro-states they contain. That doesn't mean I necessarily have any information about which macro-state the system is actually in.
  - kgwgk 4y ago
    How is a macrostate TTTTxxxx different from having the information about the TTTT part and not about the xxxx part? Talking bout the entropy of the macrostate TTTTxxxx makes sense only conditional on the TTTT information.
    - oh_my_goodness 4y ago

gota 4y ago

Oh my god, this explanation is gold. Thank you. I'm going to save it and refer to it in the future.

deltaonefour 4y ago

No this is completely and utterly wrong. Entropy is not a function of knowledge. Two people with varying and different levels of knowledge of a system does not mean the system has two different entropy values. Even if I knew the exact position of all atoms in a cup of water, the temperature of that water does not change due to that knowledge. Entropy does rely on what your picked configuration of macro states and microstates. Temperature is an arbitrary choice of macrostate.

jbay808 4y ago
> Even if I knew the exact position of all atoms in a cup of water, the temperature of that water does not change due to that knowledge. It actually does! You would disagree with the other person about the temperature of that water. But I agree that this is admittedly not obvious at first.
- deltaonefour 4y ago
  No it does not. The thermometer does not change based off of my knowledge or opinion.
  - jbay808 4y ago
    A thermometer doesn't measure temperature any better than a meterstick measures length. And we all know what Einstein had to say about the relativity of metersticks. To paraphrase from the paper I linked in another reply to you, a thermometer is just a heat bath equipped with a pointer which reads its average energy, whose scale is calibrated to give the temperature T, defined by 1/T = dS/d<E>. You can read the thermometer if you like, but if you know the exact microstate of the water to begin with, the thermometer reading will tell you much less than you already knew about the water. And precise knowledge of the water's microstate will (theoretically) allow you to extract much more work from that water than you would be able to with only the thermometer reading.
    - deltaonefour 4y ago