Geodesic
Entropy in the sense of Boltzmann and Poincar\'e
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 6, pp. 995-1029

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The $H$-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.
Keywords: Boltzmann equation, $H$-theorem, entropy, conservation laws, discrete model, Boltzmann extremal, time mean, Cesáro mean, variational principle.
Mots-clés : Liouville equation, Markov chains 
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     title = {Entropy in the sense of {Boltzmann} and {Poincar\'e}},
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V. V. Vedenyapin; S. Z. Adzhiev. Entropy in the sense of Boltzmann and Poincar\'e. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 6, pp. 995-1029. http://geodesic.mathdoc.fr/item/RM_2014_69_6_a1/