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Regul. Chaotic Dyn., 2011, Volume 16, Issue 5, Pages 536–549 (Mi rcd468)  

Statistical Irreversibility of the Kac Reversible Circular Model

Valery V. Kozlov

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

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 Boltzmannís 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 based on the analysis of weak convergence of probability distributions.

Keywords: reversibility, stochastic equilibrium, weak convergence

DOI: https://doi.org/10.1134/S1560354711050091


Bibliographic databases:

Document Type: Article
MSC: 37A60
Received: 29.10.2010
Accepted:04.12.2010
Language: English

Citation: Valery V. Kozlov, “Statistical Irreversibility of the Kac Reversible Circular Model”, Regul. Chaotic Dyn., 16:5 (2011), 536–549

Citation in format AMSBIB
\Bibitem{Koz11}
\by Valery V. Kozlov
\paper Statistical Irreversibility of the Kac Reversible Circular Model
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 5
\pages 536--549
\mathnet{http://mi.mathnet.ru/rcd468}
\crossref{https://doi.org/10.1134/S1560354711050091}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2844863}
\zmath{https://zbmath.org/?q=an:1309.37015}


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