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Nelin. Dinam., 2011, Volume 7, Number 1, Pages 101–117 (Mi nd210)  

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

Statistical irreversibility of the Kac reversible circular model

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The Kac circular model is a discrete dynamical system which has the property of recurrence and reversibility. Within the framework of this model M. Kac formulated necessary conditions for irreversibility over “short” time intervals to take place and demonstrated Boltzmann's most important exploration methods and ideas, outlining their advantages and limitations. We study the circular model within the realm of the theory of Gibbs ensembles and offer a new approach to a rigorous proof of the “zeroth” law of thermodynamics basing on the analysis of weak convergence of probability distributions.

Keywords: reversibility; stochastic equilibrium; weak convergence

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Document Type: Article
UDC: 531
MSC: 37A60
Received: 29.10.2010
Revised: 04.12.2010

Citation: V. V. Kozlov, “Statistical irreversibility of the Kac reversible circular model”, Nelin. Dinam., 7:1 (2011), 101–117

Citation in format AMSBIB
\Bibitem{Koz11}
\by V.~V.~Kozlov
\paper Statistical irreversibility of the Kac reversible circular model
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 1
\pages 101--117
\mathnet{http://mi.mathnet.ru/nd210}
\elib{http://elibrary.ru/item.asp?id=15648771}


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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. A. S. Bugaev, A. P. Buslaev, V. V. Kozlov, A. G. Tatashev, M. V. Yashina, “Obobschennaya transportno-logisticheskaya model kak klass dinamicheskikh sistem”, Matem. modelirovanie, 27:12 (2015), 65–87  mathnet  elib
    2. Kozlov V.V., Buslaev A.P., Tatashev A.G., “Monotonic Walks on a Necklace and a Coloured Dynamic Vector”, Int. J. Comput. Math., 92:9, SI (2015), 1910–1920  crossref  isi
    3. Kozlov V.V., Buslaev A.P., Tatashev A.G., Yashina M.V., “Dynamical Systems on Honeycombs”, Traffic and Granular Flow `13, eds. Chraibi M., Boltes M., Schadschneider A., Seyfried A., Springer Int Publishing Ag, 2015, 441–452  crossref  isi
  • Нелинейная динамика
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