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Kinetics of collisionless gas: equalization of temperature, growth of the coarse-grained entropy and the Gibbs paradox. (English) Zbl 1229.82092
Summary: The Poincaré model for dynamics of a collisionless gas in a rectangular parallelepiped with mirror walls is considered. The question on smoothing of the density and the temperature of this gas and conditions for the monotone growth of the coarse-grained entropy are discussed. All these effects provide a new insight of the classical paradox of mixing of gases.

MSC:
82B30 Statistical thermodynamics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
70H05 Hamilton’s equations
37A60 Dynamical aspects of statistical mechanics
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