Liouville & Entropy: Solving the Controversy

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Discussion Overview

The discussion revolves around the perceived controversy between the second law of thermodynamics and Liouville's theorem, particularly in the context of conservative systems such as gases. Participants explore the implications of these principles on entropy and the behavior of particles over time.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant questions the compatibility of the second law of thermodynamics with Liouville's theorem, suggesting that all states should eventually be reached in a conservative system.
  • Another participant argues that there is no actual controversy, stating that the thermodynamic result applies to infinite particle systems and that real systems experience fluctuations, making extreme states highly improbable.
  • A participant expresses agreement with the idea that the second law is a statistical result, proposing that it could be violated over extremely long timescales.
  • Further contributions reference the fluctuation theorem and experimental evidence suggesting that entropy can decrease temporarily, challenging the notion of the second law as an absolute principle.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement, with some supporting the statistical interpretation of the second law while others emphasize the role of fluctuations in real systems. The discussion remains unresolved regarding the implications of these viewpoints.

Contextual Notes

Participants note that the discussion hinges on assumptions about the nature of particle systems and the definitions of thermodynamic laws, as well as the conditions under which fluctuations occur.

Gerenuk
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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?
 
Gerenuk said:
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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