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.
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
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\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
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1106829}
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\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 86
\issue 1
\pages 82--89
\crossref{https://doi.org/10.1007/BF01018500}
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Linking options:
https://www.mathnet.ru/eng/tmf5427
https://www.mathnet.ru/eng/tmf/v86/i1/p120
This publication is cited in the following 7 articles:
L. D. Pustylnikov, M. V. Deryabin, “Chërnye dyry i obobschënnye relyativistskie billiardy”, Preprinty IPM im. M. V. Keldysha, 2013, 054, 36 pp.
Kushal Shah, “Large-amplitude oscillations in the rectangular Fermi accelerator”, Phys. Rev. E, 88:2 (2013)
Kushal Shah, Dmitry Turaev, Vered Rom-Kedar, “Exponential energy growth in a Fermi accelerator”, Phys. Rev. E, 81:5 (2010)
L. D. Pustyl'nikov, “The law of entropy increase and generalized billiards”, Russian Math. Surveys, 54:3 (1999), 650–651
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
T Kruger, L D Pustyl'nikov, S E Troubetzkoy, “Acceleration of bouncing balls in external fields”, Nonlinearity, 8:3 (1995), 397
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
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