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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 11, Pages 2063–2074 (Mi zvmmf9576)  
This article is cited in 25 scientific papers (total in 25 papers)

Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model

S. Z. Adzhiev, V. V. Vedenyapin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
Full-text PDF (727 kB) Citations (25)
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Abstract: Time averages are proved to coincide with Boltzmann extremals for Markov chains, discrete Liouville equations, and their generalizations. A variational principle is proposed for finding stationary solutions in these cases.
Key words: Boltzmann equation, $H$-theorem, entropy, conservation laws, discrete velocity model, Boltzmann extremal, Liouville equation, time average, Cesaro mean, Markov chains, variational principle.
Received: 08.04.2011
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 11, Pages 1942–1952
DOI: https://doi.org/10.1134/S0965542511110029
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: S. Z. Adzhiev, V. V. Vedenyapin, “Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model”, Zh. Vychisl. Mat. Mat. Fiz., 51:11 (2011), 2063–2074; Comput. Math. Math. Phys., 51:11 (2011), 1942–1952
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:54
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