H-theorem
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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 :
- <math>H \equiv \int { P ({ln P}) d^3 v} = \left\langle { ln P } \right\rangle<math>
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
- <math>S \equiv - { H \over k}<math>
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.