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This article is cited in 1 scientific paper (total in 1 paper)
Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems
Valery V. Kozlov Steklov Mathematical Institute, Russian Academy of Sciences,
ul. Gubkina 8, 119991 Moscow, Russia
Abstract:
The properties of the Gibbs ensembles of Hamiltonian systems describing the motion along geodesics on a compact configuration manifold are discussed.We introduce weakly ergodic systems for which the time average of functions on the configuration space is constant almost everywhere. Usual ergodic systems are, of course, weakly ergodic, but the converse is not true. A range of questions concerning the equalization of the density and the temperature of a Gibbs ensemble as time increases indefinitely are considered. In addition, the weak ergodicity of a billiard in a rectangular parallelepiped with a partition wall is established.
Keywords:
Hamiltonian system, Liouville and Gibbs measures, Gibbs ensemble, weak ergodicity, mixing, billiard in a polytope.
Received: 21.09.2020 Accepted: 27.10.2020
Citation:
Valery V. Kozlov, “Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems”, Regul. Chaotic Dyn., 25:6 (2020), 674–688
Linking options:
https://www.mathnet.ru/eng/rcd1090 https://www.mathnet.ru/eng/rcd/v25/i6/p674
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Abstract page: | 138 | References: | 40 |
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