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 a…
> 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 ori…
The point is pedagogical. Entropy takes a lot of time for people to understand clearly. That is the discussion from the OP. Adding "knowlege" to the definition (or to an initial explanation) of entropy makes that learning process even more difficult. And it's unnecessary. It's better than the older talk about "disorder" but it's distracting. We can bypass 'knowledge' and come back later, with no penalty and plenty of…
I think that the "microstate counting" approach - if that's what you are defending - doesn't allow to understand entropy clearly because only works for the microcanonical description. It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature. (Which is the standard thermodynamics problem.) The concept of how much can we tell about the microstate given only the pressure and te…
And of course the "knowledge" part - the entropy being a function of the probability distribution for the microstate conditional on the macrostate - is there just the same in the microstate counting approach. (Where the latter is applicable!)
If given the macrostate all microstates are equally probable we can just count them. The more there are the higher the entropy.
In general we have a probability distribution for microstates conditional on the macrostate. To have a clear understanding of entropy that should be at least mentioned.
The point is pedagogical. Entropy takes a lot of time for people to understand clearly. That is the discussion from the OP. Adding "knowlege" to the definition (or to an initial explanation) of entropy makes that learning process even more difficult. And it's unnecessary. It's better than the older talk about "disorder" but it's distracting. We can bypass 'knowledge' and come back later, with no penalty and plenty of…
I think that the "microstate counting" approach - if that's what you are defending - doesn't allow to understand entropy clearly because only works for the microcanonical description. It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature. (Which is the standard thermodynamics problem.) The concept of how much can we tell about the microstate given only the pressure and te…
> It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature.
But nobody does that since the total value of entropy isn't important. What you do is count the factor difference in count of microstates between two volumes, that is what you care about, and it is easy to see how the number of microstates changes when you double the volume or other similar changes.
I think that the "microstate counting" approach - if that's what you are defending - doesn't allow to understand entropy clearly because only works for the microcanonical description. It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature. (Which is the standard thermodynamics problem.) The concept of how much can we tell about the microstate given only the pressure and te…
> It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature. But nobody does that since the total value of entropy isn't important. What you do is count the factor difference in count of microstates between two volumes, that is what you care about, and it is easy to see how the number of microstates changes when you double the volume or other similar changes.
Is it easy to see how the number of microstates changes when you increase the temperature - everything else being equal?
How would you say that it changes then?
I'd say that the number of compatible microstates doesn't change. The probability of each microstate does change though.
> 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 ther…
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 mic…
> 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.
> 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 ther…
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 mic…
> 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.
If you knew the exact position of all atoms in a cup of water you wouldn't assign any temperature to it. Not a thermodynamic temperature at least.
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,…
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.
I respectfully disagree. Perhaps you'd like to present more than a mere assertion to make your case. I did.
> It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature. But nobody does that since the total value of entropy isn't important. What you do is count the factor difference in count of microstates between two volumes, that is what you care about, and it is easy to see how the number of microstates changes when you double the volume or other similar changes.
Is it easy to see how the number of microstates changes when you increase the temperature - everything else being equal? How would you say that it changes then? I'd say that the number of compatible microstates doesn't change. The probability of each microstate does change though.
Your statement doesn't make sense, temperature is defined in terms of entropy changes, you can't calculate temperature without first calculating entropy changes.
Is it easy to see how the number of microstates changes when you increase the temperature - everything else being equal? How would you say that it changes then? I'd say that the number of compatible microstates doesn't change. The probability of each microstate does change though.
Your statement doesn't make sense, temperature is defined in terms of entropy changes, you can't calculate temperature without first calculating entropy changes.
Have you heard of thermometers? I can have a container with 1l of some gas at room temperature T1 and proceed to heat the room - and the container - to temperature T2.
How do you calculate the number of microstates for the sample of gas before and after? How do you think these numbers are related? You said it was easy!
I don't understand entropy and this article did not change it. The issue I take is with the definition of "the most likely state". Think of a series of random bits that can be either 0 or 1 with equal probability. How likely is it that they are all 0 or all 1? Not very likely. There is exactly one configuration. How likely is it that they have a specific configuration of 0 and 1? Equally likely. All states are equall…
This is a very sensible confusion. The forms of macroscopic averaging functions which are useful and valid cannot be made up arbitrarily, but are determined by the microscopic physical laws of the system. There is a reason that the law of increase of entropy is the second law of classical thermodynamics, with conservation of energy being the first law. To state it explicitly: energy is a globally conserved quantity, which can be freely exchanged among the interacting microscopic parts of systems. So we can bring a test system (called a thermometer) into interaction with our system under study, (indirectly) observe the average energy per degree of freedom of the thermometer, and call that observation the temperature of the system under study. Similarly, it is a known physical phenomenon that a gas confined to a container will exert a steady average outward force per normal unit area on the walls of the container; we have ways to measure this force, and we call it pressure. And so on, and on: every useful macroscopic averaging function is a relatively stable, measurable quantity which is determined by the physics of the systems under study. If we discovered some new measurement technique tomorrow which enabled us to measure the "quintessence" of physical systems, and this measurement was stable and reproducible, and could be meaningfully aggregated from the microscopic parts of the system and measured on the macroscopic scale, our definition of entropy would change, to account for "quintessence".