3 ms·

Equilibrium is local in your example. Globally, the rush of air from one side to the other would result in detectable oscillations whose released energy could

Equilibrium is local in your example. Globally, the rush of air from one side to the other would result in detectable oscillations whose released energy could be used to determine which chamber was initially empty, assuming one can find and isolate the information.

AnimalMuppet 5y ago
I see. All right, I put oxygen at some pressure on one side, and nitrogen at the same pressure on the other side, and then remove the barrier. Now there are no oscillations, just mixing.
- danbruc 5y ago
  This doesn't change the situation. Shortly after removing the barrier, some molecules will start moving into the other half. Just reverse all velocities and see all the molecules move back into the half they started in. If you go further forward in time, you will eventually see the first collision. But that doesn't really change the situation, reverse the velocities, see the molecules collide in reverse and then move back into their starting halfs. And this never really changes, particles move and collide and this can be reversed, you just have to do this for very, very many particles and collisions. And this is probably chaotic, the tiniest error in any of the positions or velocities will get massively amplified and give you the wrong initial state. But in principle it could be done. And it has to be done on the microscopic level, macroscopic things like concentrations, temperatures, or pressures by definition do not reflect the microscopic states.
- SkyBelow 5y ago
  If you know the information about every single molecule of each, you could calculate backwards the probability of where they came from. Eventually you would reach a state where the most likely probability would show all the oxygen on one side and all the nitrogen on the other. This is a purely theoretical calculation, far outside the scope of our ability to calculate. It is one of those, if we turned all known matter into the possible fastest computer, could that even calculate it before the heat death of the universe sorts of questions.

AnimalMuppet 5y ago

I see. All right, I put oxygen at some pressure on one side, and nitrogen at the same pressure on the other side, and then remove the barrier. Now there are no oscillations, just mixing.

danbruc 5y ago
This doesn't change the situation. Shortly after removing the barrier, some molecules will start moving into the other half. Just reverse all velocities and see all the molecules move back into the half they started in. If you go further forward in time, you will eventually see the first collision. But that doesn't really change the situation, reverse the velocities, see the molecules collide in reverse and then move back into their starting halfs. And this never really changes, particles move and collide and this can be reversed, you just have to do this for very, very many particles and collisions. And this is probably chaotic, the tiniest error in any of the positions or velocities will get massively amplified and give you the wrong initial state. But in principle it could be done. And it has to be done on the microscopic level, macroscopic things like concentrations, temperatures, or pressures by definition do not reflect the microscopic states.
SkyBelow 5y ago
If you know the information about every single molecule of each, you could calculate backwards the probability of where they came from. Eventually you would reach a state where the most likely probability would show all the oxygen on one side and all the nitrogen on the other. This is a purely theoretical calculation, far outside the scope of our ability to calculate. It is one of those, if we turned all known matter into the possible fastest computer, could that even calculate it before the heat death of the universe sorts of questions.