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

  • Nagi KhalilEmail author


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.


Adiabatic piston Kinetic theory Boltzmann equation \({\mathcal {H}}\)-theorem 

Mathematics Subject Classification

70Fxx 82B40 82C40 82D05 



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


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Authors and Affiliations

  1. 1.IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas ComplejosCampus Universitat de les Illes BalearsPalmaSpain

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