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Deterministic Motion of the Controversial Piston in the Thermodynamic Limit

Gruber, Christian ; Pache, Séverine ; Lesne, Annick

In: Journal of Statistical Physics, 2002, vol. 108, no. 3-4, p. 669-701

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    Titre
    • Deterministic Motion of the Controversial Piston in the Thermodynamic Limit
    Auteur
    • Gruber, Christian. Institut de Physique Théorique, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
    • Pache, Séverine. Institut de Physique Théorique, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
    • Lesne, Annick. Université Pierre et Marie Curie, Case courrier 121, 4 Place Jussieu, 75252, Paris Cedex 05, France
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Statistical Physics, 2002, vol. 108, no. 3-4, p. 669-701. Kluwer Academic Publishers-Plenum Publishers
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:321447
    Summary
    We consider the evolution of a system composed of N non-interacting point particles of mass m in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area A of the cross-section, the mass M of the piston, and the number N of particles go to infinity keeping A/M and N/M fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption