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Billiards, invariant measures, and equilibrium thermodynamics. II. (English) Zbl 1078.82012
Summary: The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that, in this case, all the fundamental relations for a multidimensional ideal gas in thermal equilibrium hold true.
Part I, see ibid. 5, No. 2, 129–138 (2000; Zbl 1050.82028).

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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