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Mesoscopic Description of the Adiabatic Piston: Kinetic Equations and \({\mathcal {H}}\)-Theorem

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Abstract

The adiabatic piston problem is solved at the mesoscale using a kinetic theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston). A closed system of equations for the distribution functions of the gases conditioned to a position of the piston and the distribution function of the piston is derived, under the assumption of a generalized molecular chaos. It is shown that the resulting kinetic description has the canonical equilibrium as a steady-state solution. Moreover, the Boltzmann entropy, which includes the motion of the piston, verifies the \({\mathcal {H}}\)-theorem. The kinetic description is not limited to the thermodynamic limit nor to a small ratio between the masses of the particle and the piston, and collisions among particles are explicitly considered.

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Acknowledgements

I dedicate this work to the memory of María José Ruiz Montero.

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  1. IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, 07122, Palma, Spain

    Nagi Khalil

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  1. Nagi Khalil
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Correspondence to Nagi Khalil.

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Communicated by Abhishek Dhar.

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Khalil, N. Mesoscopic Description of the Adiabatic Piston: Kinetic Equations and \({\mathcal {H}}\)-Theorem. J Stat Phys 176, 1138–1160 (2019). https://doi.org/10.1007/s10955-019-02336-x

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  • DOI: https://doi.org/10.1007/s10955-019-02336-x

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