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H-theoremIn 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 Boltmann equation one can proved 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.
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