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Regul. Chaotic Dyn., 2008, Volume 13, Issue 3, Pages 141–154 (Mi rcd566)  

This article is cited in 3 scientific papers (total in 3 papers)

Gibbs Ensembles, Equidistribution of the Energy of Sympathetic Oscillators and Statistical Models of Thermostat

V. V. Kozlov

V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: The paper develops an approach to the proof of the "zeroth" law of thermodynamics. The approach is based on the analysis of weak limits of solutions to the Liouville equation as time grows infinitely. A class of linear oscillating systems is indicated for which the average energy becomes eventually uniformly distributed among the degrees of freedom for any initial probability density functions. An example of such systems are sympathetic pendulums. Conditions are found for nonlinear Hamiltonian systems with finite number of degrees of freedom to converge in a weak sense to the state where the mean energies of the interacting subsystems are the same. Some issues related to statistical models of the thermostat are discussed.

Keywords: Hamiltonian system, sympathetic oscillators, weak convergence, thermostat

DOI: https://doi.org/10.1134/S1560354708030015


Bibliographic databases:

MSC: 37A60, 60K35, 70H05, 82B30, 40A9
Received: 13.06.2007
Accepted:28.10.2007
Language:

Citation: V. V. Kozlov, “Gibbs Ensembles, Equidistribution of the Energy of Sympathetic Oscillators and Statistical Models of Thermostat”, Regul. Chaotic Dyn., 13:3 (2008), 141–154

Citation in format AMSBIB
\Bibitem{Koz08}
\by V.~V.~Kozlov
\paper Gibbs Ensembles, Equidistribution of the Energy of Sympathetic Oscillators and Statistical Models of Thermostat
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 141--154
\mathnet{http://mi.mathnet.ru/rcd566}
\crossref{https://doi.org/10.1134/S1560354708030015}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2415369}
\zmath{https://zbmath.org/?q=an:1229.82091}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Andrea Carati, Luigi Galgani, Alberto Maiocchi, Fabrizio Gangemi, Roberto Gangemi, “The FPU Problem as a Statistical-mechanical Counterpart of the KAM Problem, and Its Relevance for the Foundations of Physics”, Regul. Chaotic Dyn., 23:6 (2018), 704–719  mathnet  crossref
    2. A. L. Kuzemsky, “Nonequilibrium statistical operator method and generalized kinetic equations”, Theoret. and Math. Phys., 194:1 (2018), 30–56  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Carati A. Galgani L. Gangemi F. Gangemi R., “Relaxation Times and Ergodic Properties in a Realistic Ionic-Crystal Model, and the Modern Form of the Fpu Problem”, Physica A, 532 (2019), 121911  crossref  isi  scopus
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