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Zbl 1230.82006
Morimoto, Tetsuzo
On the $H$-theorem from the standpoint of classical mechanics. (English)
[J] J. Phys. Soc. Japan 22, No. 6, 1362-1364 (1967). ISSN 0031-9015; ISSN 1347-4073/e

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 2000:: *82B03 Foundations of equilibrium statistical mechanics
37A99 Ergodic theory

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Zentralblatt MATH Berlin [Germany]