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.