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 TMF, 1991, Volume 86, Number 1, Pages 120–129 (Mi tmf5427)

A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics

L. D. Pustyl'nikov

Abstract: A mechanism of occurrence of irreversibility is found. It is based on allowance for the relativistic factor in a mechanical system consisting of a finite number of particles interacting with one another in accordance with the law of elastic collision and moving in a container of fixed volume with a natural law of reflection from the container walls. A new concept of thermodynamic entropy of the system is introduced, and it is shown that for fairly general conditions both the new entropy and the Gibbs entropy for this system of particles increases unboundedly with the time when the relativistic factor is taken into account, whereas when it is not the new entropy is constant, not dependent on the time, while the Gibbs entropy fluctuates in a bounded range as the time increases without limit. It is also shown that in the relativistic case the energy of all the particles tends to infinity exponentially with the time.

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English version:
Theoretical and Mathematical Physics, 1991, 86:1, 82–89

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Citation: L. D. Pustyl'nikov, “A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics”, TMF, 86:1 (1991), 120–129; Theoret. and Math. Phys., 86:1 (1991), 82–89

Citation in format AMSBIB
\Bibitem{Pus91} \by L.~D.~Pustyl'nikov \paper A~mechanism of irreversibility and unbounded growth of the energy in a~model of statistical mechanics \jour TMF \yr 1991 \vol 86 \issue 1 \pages 120--129 \mathnet{http://mi.mathnet.ru/tmf5427} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1106829} \zmath{https://zbmath.org/?q=an:0987.82504} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 1 \pages 82--89 \crossref{https://doi.org/10.1007/BF01018500} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GC79000010} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. D. Pustyl'nikov, “Existence of invariant curves for maps close to degenerate maps, and a solution of the Fermi–Ulam problem”, Russian Acad. Sci. Sb. Math., 82:1 (1995), 231–241
2. L. D. Pustyl'nikov, “Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism”, Russian Math. Surveys, 50:1 (1995), 145–189
3. L. D. Pustyl'nikov, “The law of entropy increase and generalized billiards”, Russian Math. Surveys, 54:3 (1999), 650–651
4. L. D. Pustylnikov, M. V. Deryabin, “Chërnye dyry i obobschënnye relyativistskie billiardy”, Preprinty IPM im. M. V. Keldysha, 2013, 054, 36 pp.
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