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Russian Mathematical Surveys, 2014, Volume 69, Issue 6, Pages 995–1029
DOI: https://doi.org/10.1070/RM2014v069n06ABEH004926 (Mi rm9635) 		 
This article is cited in 35 scientific papers (total in 35 papers)

Entropy in the sense of Boltzmann and Poincaré

V. V. Vedenyapina, S. Z. Adzhievb

a Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
b Moscow State University
English version PDF (739 kB) Citations (35)
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DOI: https://doi.org/10.1070/RM2014v069n06ABEH004926
Abstract: 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, Liouville equation, time mean, Cesáro mean, Markov chains, variational principle.
Received: 13.10.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2014, Volume 69, Issue 6(420), Pages 45–80
DOI: https://doi.org/10.4213/rm9635
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: Primary 60K30, 80A30; Secondary 60J27, 82C22, 82C40, 92E20
Language: English
Original paper language: Russian
Citation: V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Uspekhi Mat. Nauk, 69:6(420) (2014), 45–80; Russian Math. Surveys, 69:6 (2014), 995–1029
Citation in format AMSBIB
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    • This publication is cited in the following 35 articles:
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