## On the $$H$$-theorem from the standpoint of classical mechanics.(English)Zbl 1230.82006

Summary: We prove that the statistical mechanical phenomena in the ergodic system are always irreversible when the system has no “angle variables”. Firstly it is shown by using the theorems due to Koopman-von Neumann-Hopf that for such a system $$H$$-function is never less than its time average and then it can be concluded that the $$H$$-theorem always holds.

### MSC:

 82B03 Foundations of equilibrium statistical mechanics 37A99 Ergodic theory
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