Poincaré recurrence and maximum entropy

[cryptist]

Fluctuation theorem says that there will be fluctuations in microscopic scale that results local decreases in entropy even in isolated systems. According to the Poincaré recurrence theorem, after sufficiently long time, any finite system can turn into a state which is very close to its initial state. It means second law of thermodynamics will be broken in even macroscopic scale.

We can always observe fluctuations in non-equilibrium systems, however, my question is; If a system eventually reaches to the maximum entropy state (everything is in absolute equilibrium), then do we expect fluctuations even in that state? Or after reaching maximum entropy, the system will remain same always or not? In other words, does Poincaré recurrence theorem valid for systems with maximum possible entropy?

 

[mfb]

It means second law of thermodynamics will be broken in even macroscopic scale.

The timescale just influences the size of the "violations" you can get.

If a system eventually reaches to the maximum entropy state (everything is in absolute equilibrium), then do we expect fluctuations even in that state?

Sure.

 

[ImaLooser]

Fluctuation theorem says that there will be fluctuations in microscopic scale that results local decreases in entropy even in isolated systems. According to the Poincaré recurrence theorem, after sufficiently long time, any finite system can turn into a state which is very close to its initial state. It means second law of thermodynamics will be broken in even macroscopic scale.

We can always observe fluctuations in non-equilibrium systems, however, my question is; If a system eventually reaches to the maximum entropy state (everything is in absolute equilibrium), then do we expect fluctuations even in that state? Or after reaching maximum entropy, the system will remain same always or not? In other words, does Poincaré recurrence theorem valid for systems with maximum possible entropy?

This is all true, but macroscopic system are so large that you will never observe a significant deviation.

 

[Chalnoth]

We can always observe fluctuations in non-equilibrium systems, however, my question is; If a system eventually reaches to the maximum entropy state (everything is in absolute equilibrium), then do we expect fluctuations even in that state? Or after reaching maximum entropy, the system will remain same always or not? In other words, does Poincaré recurrence theorem valid for systems with maximum possible entropy?

The difference between a high entropy state and a low entropy state is that a fluctuation in a low entropy state is very likely to increase the entropy, leading to a system that looks somewhat different. By contrast, a fluctuation in a high-entropy state is very likely to lead to a another state that has just as much entropy (this is what makes a state high entropy in the first place: most possible configurations of the system are high entropy configurations).

So the fluctuations are always ongoing, it's just that once equilibrium is reached, further fluctuations just lead to different microscopic configurations that look like the same equilibrium state.

That said, a fluctuation from a high entropy state will not always lead to another high entropy state. Occasionally low entropy states will occur. But these are rare, because there just aren't that many low entropy configurations available.

 

[cryptist]

I think I get my answer; there is always a possibility of fluctuations even system reaches its maximum entropy state.

Thank you all for your answers.