Entropy in the sense of Boltzmann and Poincaré

Abstract

The -theorem is proved for generalized equations of chemical kinetics, and important physical examples of such generalizations are considered: a discrete model of the quantum kinetic equations (the Uehling– Uhlenbeck equations) and a quantum Markov process (a quantum random walk). The time means are shown to coincide with the Boltzmann extremals for these equations and for the Liouville equation. Bibliography: 41 titles.