This article is cited in 4 scientific papers (total in 4 papers)
A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics
L. D. Pustyl'nikov
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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Theoretical and Mathematical Physics, 1991, 86:1, 82–89
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
\paper A~mechanism of irreversibility and unbounded growth of the energy in a~model of statistical mechanics
\jour Theoret. and Math. Phys.
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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
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
L. D. Pustyl'nikov, “The law of entropy increase and generalized billiards”, Russian Math. Surveys, 54:3 (1999), 650–651
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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