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The statistical mechanics of a class of dissipative systems. (English. Russian original) Zbl 1272.82004
J. Appl. Math. Mech. 76, No. 1, 15-24 (2012); translation from Prikl. Mat. Mekh. 76, No. 1, 23-35 (2012).
Summary: The statistical mechanics of dynamical systems on which only isotropic viscous friction forces act is developed. A non-stationary analogue of the Gibbs canonical distribution, which enables each such system to be made to correspond to a certain thermodynamic system that satisfies the first and second laws of thermodynamics, is introduced. The evolution of non-Gibbs probability distributions with time is also considered.
MSC:
82B05 Classical equilibrium statistical mechanics (general)
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References:
[1] Appell, P., Traité de Mécanique rationnelle, vol. 2: dynamique des systèmes. Mécanique analytique, (1931), Gauthier-Villars Paris · JFM 35.0692.01
[2] Arzhanykh, I.S., Momentum fields, (1971), National Lending Library for Science and Technology Boston Spa · Zbl 0225.70001
[3] Kozlov, V.V., Hydrodynamic theory of a class of finite-dimensional dissipative systems, Tr mat inst im V A steklova, 223, 181-186, (1998) · Zbl 1195.70024
[4] Gibbs, J.W., Elementary principles in statistical mechanics, (1902), Scribner New York · JFM 33.0708.01
[5] Kozlov, V.V., Billiards, invariant measures, and equilibrium thermodynamics. II, Reg chaotic dyn, 9, 2, 91-100, (2004) · Zbl 1078.82012
[6] Kozlov, V.V., Kinetics of a collisionless continuous medium, Reg chaotic dyn, 6, 3, 235-251, (2001) · Zbl 1006.82011
[7] Kozlov, V.V., Statistical properties of billiards and polyhedra, Dokl akad nauk, 416, 3, 302-305, (2007)
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