Geodesic
Kinetics of collisionless gas: equalization of temperature, growth of the coarse-grained entropy and the Gibbs paradox
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 3, pp. 377-383.

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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.
Keywords: collisionless gas, coarse-grained entropy, Gibbs paradox. 
@article{ND_2009_5_3_a4,
     author = {V. V. Kozlov},
     title = {Kinetics of collisionless gas: equalization of temperature, growth of the coarse-grained entropy and the {Gibbs} paradox},
     journal = {Russian journal of nonlinear dynamics},
     pages = {377--383},
     publisher = {mathdoc},
     volume = {5},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/ND_2009_5_3_a4/}
}
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V. V. Kozlov. Kinetics of collisionless gas: equalization of temperature, growth of the coarse-grained entropy and the Gibbs paradox. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 3, pp. 377-383. http://geodesic.mathdoc.fr/item/ND_2009_5_3_a4/