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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive
Zh. Vychisl. Mat. Mat. Fiz., 2011 Volume 51, Number 11, Pages 2063–2074 (Mi zvmmf9576)
This article is cited 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

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.

UDC: 519.676

Received: 08.04.2011


 English version: Computational Mathematics and Mathematical Physics, 2011, 51:11, 1942–1952

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© Steklov Math. Inst. of RAS, 2024