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 based on the analysis of weak convergence of probability distributions.
\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://mathscinet.ams.org/mathscinet-getitem?mr=2844863}
\zmath{https://zbmath.org/?q=an:1309.37015}
Linking options:
https://www.mathnet.ru/eng/rcd468
https://www.mathnet.ru/eng/rcd/v16/i5/p536
This publication is cited in the following 3 articles:
A. S. Trushechkin, “Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems”, Proc. Steklov Inst. Math., 324 (2024), 187–212
Valery V. Kozlov, “Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems”, Regul. Chaotic Dyn., 25:6 (2020), 674–688
A.Yu. Zakharov, “Determinism vs. statistics in classical many-body theory: Dynamical origin of irreversibility”, Physica A: Statistical Mechanics and its Applications, 473 (2017), 72
Citation in format AMSBIB
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