Entropy is, broadly speaking, a statement of the irreversibility of forces.
As long as you’re sticking to classical physics, the fundamental laws are invariant under time reversal. So in what sense are forces “irreversible”? Take Newtonian gravitation, an example you use. If you take the time reverse of a world where massive particles interact according to Newton’s law of gravitation, the resulting time-reversed world will also be one where massive particles interact according to Newton’s law of gravitation. The fundamental forces do not pick out a direction of time, so how can they be the foundation for the entropic arrow of time?
In a closed solar system, gravity means that eventually, everything will be in a stable configuration; a single concentrated ball, or dead objects orbiting each other. There are several stable configurations, but each are local entropic maximums.
This claim, read literally, is false. It contradicts Liouville’s theorem. The theorem says that in a Hamiltonian system, there cannot be a compression of accessible phase space with time. This means that our system cannot have any attractors or limit cycles. You, on the other hand, are saying that a closed solar system has attractors (a single concentrated ball) and limit cycles (dead objects orbiting each other). Basically you are saying that points of phase space which used to be available to the system (points that do not correspond to a single ball or stable orbits) will eventually become unavailable. This entails that phase space is being compressed.
The connection you are trying to draw between entropy and forces is not standard statistical mechanics. In fact, unless I am misinterpreting what you are saying, it contradicts standard statistical mechanics.
The fundamental forces do not pick out a direction of time, so how can they be the foundation for the entropic arrow of time?
I’m assuming that the law of entropy is obeyed. That bit about “Entropy being the product of forces” is important.
This claim, read literally, is false. It contradicts Liouville’s theorem. The theorem says that in a Hamiltonian system, there cannot be a compression of accessible phase space with time.
The universe is not a Hamiltonian system. We have gravity, we have heat. Moreover, the phase space is maintained in the microstates.
I’m assuming that the law of entropy is obeyed. That bit about “Entropy being the product of forces” is important.
Your statement of the law of entropy is “Forces do what forces do”. But the forces are doing what they do in the time reversed scenario as well. The forces don’t change when you reverse time. So if the law of entropy is that forces do what they do, then why doesn’t it hold in the time-reversed scenario?
When you say that entropy is the product of forces, I presume you mean that entropy increase is the product of forces acting (if that’s now what you mean, then I don’t know how to interpret your claim). My point is that entropy increase can’t simply be a product of forces acting, because the time reversed situation is one in which the exact same forces act, yet entropy decreases. So entropy increase can’t be derived from the force laws. But if the law of entropy is an independent law above and beyond the force laws, then in what sense is entropy the product of forces?
Perhaps all you mean is that there is no separate pressure that drives systems towards higher entropy states; that the only forces acting on systems are the fundamental forces, and the increase of entropy is a consequence of those forces acting. In this attenuated sense, it is true that entropy increase is the product of the forces acting, just as it is true that natural selection is the product of the forces acting or that business cycles are the product of the forces acting. If this is your point, it is getting occluded by your presentation. Saying things like “expressions of entropy are expressions of particular forces” suggests that you’re making a different (and false) point.
The universe is not a Hamiltonian system.
Yes, but in the bit I quoted, you were talking about a closed solar system, not the universe. A closed solar system governed by Newtonian gravitation is a Hamiltonian system.
We have gravity, we have heat.
Gravitational systems are Hamiltonian. It is true that if a system dissipates heat it will not be Hamiltonian, but a closed solar system will not dissipate heat by definition, unless you mean something different by “closed” than standard physics usage.
Moreover, the phase space is maintained in the microstates.
Not sure why this relevant. There is a proper subset of phase space that corresponds to equilibrium macrostates. You are suggesting that no matter where in phase space the system begins, it will eventually end up somewhere in this subset and will remain within this subset. This contradicts Liouville’s theorem.
I’ve deleted the post, so it doesn’t matter too much, but I’ll respond anyways:
This interpretation:
“Perhaps all you mean is that there is no separate pressure that drives systems towards higher entropy states; that the only forces acting on systems are the fundamental forces, and the increase of entropy is a consequence of those forces acting. In this attenuated sense, it is true that entropy increase is the product of the forces acting, just as it is true that natural selection is the product of the forces acting or that business cycles are the product of the forces acting. If this is your point, it is getting occluded by your presentation. Saying things like “expressions of entropy are expressions of particular forces” suggests that you’re making a different (and false) point.”
is correct, however I’ll disagree about what my point suggests, as I regard my construction as semantically identical to “entropy increase is the product of the forces acting”. There might be jargon I’m misusing, though, as I’m prone to that, so I have to concede there might be an implication I’m missing.
The point of my post was effectively that the law of entropy -isn’t- an independent law; my elaborate and failed constructions were attempts to demonstrate this by reversing the law and showing that all the other laws of physics would necessarily stop working.
For the second point, I’ll just repeat that I wasn’t discussing a Hamiltonian system. A closed solar system isn’t Hamiltonian unless you treat planets and the sun as point-masses, which I wasn’t doing; gravitational tides in the particulate composition of planets slowly rob the system of momentum and convert it to heat. The whole thing eventually collapses on itself. This is the kind of situation I was trying to discuss. I guess I failed on that count as well. Shrug
As long as you’re sticking to classical physics, the fundamental laws are invariant under time reversal. So in what sense are forces “irreversible”? Take Newtonian gravitation, an example you use. If you take the time reverse of a world where massive particles interact according to Newton’s law of gravitation, the resulting time-reversed world will also be one where massive particles interact according to Newton’s law of gravitation. The fundamental forces do not pick out a direction of time, so how can they be the foundation for the entropic arrow of time?
This is probably not what OrphanWilde wanted to mean with his statement, but I agree with you that it does seem incorrect the way it’s stated, (classical) forces are indeed symmetric in time. As it’s written, it looks like the increase in entropy is caused by the various forces defining an arrow of time. Instead they’re more like two faces of the same medal: we see the forces operating in one time direction and we see an increase in entropy in the same direction. The same laws for the forces, with a reverse arrow of time, would cause a decrease in entropy. So, once you pick a preferred direction for the arrow of time, the laws for the forces dictate how entropy should evolve, but they don’t choose the direction of the arrow for themselves.
As long as you’re sticking to classical physics, the fundamental laws are invariant under time reversal. So in what sense are forces “irreversible”? Take Newtonian gravitation, an example you use. If you take the time reverse of a world where massive particles interact according to Newton’s law of gravitation, the resulting time-reversed world will also be one where massive particles interact according to Newton’s law of gravitation. The fundamental forces do not pick out a direction of time, so how can they be the foundation for the entropic arrow of time?
This claim, read literally, is false. It contradicts Liouville’s theorem. The theorem says that in a Hamiltonian system, there cannot be a compression of accessible phase space with time. This means that our system cannot have any attractors or limit cycles. You, on the other hand, are saying that a closed solar system has attractors (a single concentrated ball) and limit cycles (dead objects orbiting each other). Basically you are saying that points of phase space which used to be available to the system (points that do not correspond to a single ball or stable orbits) will eventually become unavailable. This entails that phase space is being compressed.
The connection you are trying to draw between entropy and forces is not standard statistical mechanics. In fact, unless I am misinterpreting what you are saying, it contradicts standard statistical mechanics.
The fundamental forces do not pick out a direction of time, so how can they be the foundation for the entropic arrow of time?
I’m assuming that the law of entropy is obeyed. That bit about “Entropy being the product of forces” is important.
This claim, read literally, is false. It contradicts Liouville’s theorem. The theorem says that in a Hamiltonian system, there cannot be a compression of accessible phase space with time.
The universe is not a Hamiltonian system. We have gravity, we have heat. Moreover, the phase space is maintained in the microstates.
Your statement of the law of entropy is “Forces do what forces do”. But the forces are doing what they do in the time reversed scenario as well. The forces don’t change when you reverse time. So if the law of entropy is that forces do what they do, then why doesn’t it hold in the time-reversed scenario?
When you say that entropy is the product of forces, I presume you mean that entropy increase is the product of forces acting (if that’s now what you mean, then I don’t know how to interpret your claim). My point is that entropy increase can’t simply be a product of forces acting, because the time reversed situation is one in which the exact same forces act, yet entropy decreases. So entropy increase can’t be derived from the force laws. But if the law of entropy is an independent law above and beyond the force laws, then in what sense is entropy the product of forces?
Perhaps all you mean is that there is no separate pressure that drives systems towards higher entropy states; that the only forces acting on systems are the fundamental forces, and the increase of entropy is a consequence of those forces acting. In this attenuated sense, it is true that entropy increase is the product of the forces acting, just as it is true that natural selection is the product of the forces acting or that business cycles are the product of the forces acting. If this is your point, it is getting occluded by your presentation. Saying things like “expressions of entropy are expressions of particular forces” suggests that you’re making a different (and false) point.
Yes, but in the bit I quoted, you were talking about a closed solar system, not the universe. A closed solar system governed by Newtonian gravitation is a Hamiltonian system.
Gravitational systems are Hamiltonian. It is true that if a system dissipates heat it will not be Hamiltonian, but a closed solar system will not dissipate heat by definition, unless you mean something different by “closed” than standard physics usage.
Not sure why this relevant. There is a proper subset of phase space that corresponds to equilibrium macrostates. You are suggesting that no matter where in phase space the system begins, it will eventually end up somewhere in this subset and will remain within this subset. This contradicts Liouville’s theorem.
I’ve deleted the post, so it doesn’t matter too much, but I’ll respond anyways:
This interpretation:
“Perhaps all you mean is that there is no separate pressure that drives systems towards higher entropy states; that the only forces acting on systems are the fundamental forces, and the increase of entropy is a consequence of those forces acting. In this attenuated sense, it is true that entropy increase is the product of the forces acting, just as it is true that natural selection is the product of the forces acting or that business cycles are the product of the forces acting. If this is your point, it is getting occluded by your presentation. Saying things like “expressions of entropy are expressions of particular forces” suggests that you’re making a different (and false) point.”
is correct, however I’ll disagree about what my point suggests, as I regard my construction as semantically identical to “entropy increase is the product of the forces acting”. There might be jargon I’m misusing, though, as I’m prone to that, so I have to concede there might be an implication I’m missing.
The point of my post was effectively that the law of entropy -isn’t- an independent law; my elaborate and failed constructions were attempts to demonstrate this by reversing the law and showing that all the other laws of physics would necessarily stop working.
For the second point, I’ll just repeat that I wasn’t discussing a Hamiltonian system. A closed solar system isn’t Hamiltonian unless you treat planets and the sun as point-masses, which I wasn’t doing; gravitational tides in the particulate composition of planets slowly rob the system of momentum and convert it to heat. The whole thing eventually collapses on itself. This is the kind of situation I was trying to discuss. I guess I failed on that count as well. Shrug
This is probably not what OrphanWilde wanted to mean with his statement, but I agree with you that it does seem incorrect the way it’s stated, (classical) forces are indeed symmetric in time. As it’s written, it looks like the increase in entropy is caused by the various forces defining an arrow of time. Instead they’re more like two faces of the same medal: we see the forces operating in one time direction and we see an increase in entropy in the same direction. The same laws for the forces, with a reverse arrow of time, would cause a decrease in entropy. So, once you pick a preferred direction for the arrow of time, the laws for the forces dictate how entropy should evolve, but they don’t choose the direction of the arrow for themselves.