# Liouville and Entropy

## Main Question or Discussion Point

Next to all recent Entropy thread I'd also like to have a question solved.

What's the solution to the controversy between the second law of thermodynamics, and Liouville's theorem that for conservative systems (as a gas should be?!) every state should be reached at some point? So eventually after an extraordinary long time all molecules would also gather in the corner.

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I don't think there is a controversy. The strict "thermodynamic" result is
only valid for an infinite number of particles (thus, no fluctuations). Real
systems do fluctuate though; all particles gathering in one place would be
a BIG fluctuation, thus very low probability, thus something that would only
happen after a very, very long time.

OK, that's also my favourite interpretation.

So the second law is rather a statistical result and in an extremely long period of time the second law could be arbitrarily violated?!

Any objections from someone else?

fluidistic
Gold Member
OK, that's also my favourite interpretation.

So the second law is rather a statistical result and in an extremely long period of time the second law could be arbitrarily violated?!

Any objections from someone else?
You're right. I've posted a few questions of the same kind. For instance, see https://www.physicsforums.com/showthread.php?t=319633.
See the fluctuation theorem. There was a paper about an experiment that showed entropy decreases macroscopically for a few seconds... The paper was accessible from wikipedia. The Second Law is not a "fundamental law".
I just found something related to the article: http://www.newscientist.com/article/dn2572-second-law-of-thermodynamics-broken.html.

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