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H-theorem
In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation.
The quantity H is defined as the integral over velocity space :
where P(r) is the probability. Using the Boltzmann equation one can prove that H can only decrease.
Therefore, the generalized entropy is defined as
where S always increases.
This theorem is based on Boltzmann's assumption of "molecular chaos " which breaks time reversal symmetry and therefore "begs the question".
The final resolution of the time reversibility paradox - Loschmidt's paradox - is found in the Fluctuation Theorem.
12-19-2008 14:25:18
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details