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
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