Liouville & Entropy: Solving the Controversy

[Gerenuk]

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.

 

[Oudeis Eimi]

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.

 

[Gerenuk]

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]

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.