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Regul. Chaotic Dyn., 2020, Volume 25, Issue 6, Pages 674–688 (Mi rcd1090)  

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

Funding Agency Grant Number
Russian Science Foundation 19-71- 30012
The research was funded by a grant from the Russian Science Foundation (Project No. 19-71-30012).


DOI: https://doi.org/10.1134/S1560354720060118

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Bibliographic databases:

MSC: 82C03, 82C23, 82C40
Received: 21.09.2020
Accepted:27.10.2020
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Citation: Valery V. Kozlov, “Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems”, Regul. Chaotic Dyn., 25:6 (2020), 674–688

Citation in format AMSBIB
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\by Valery V. Kozlov
\paper Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 6
\pages 674--688
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