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Stationary states for a mechanical system with stochastic boundary conditions

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Abstract

We consider a system of Newtonian particles, with a long-range repulsive pair potential, moving in a cavity whose surface temperature is spatially varying. When a particle hits the surface, it is “thermalized” at the temperature of the collision point. We prove that this system has a unique stationary ensemble, to which any initial distribution converges for large times. We show that this stationary ensemble depends continuously on the surface temperature profile.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, New Jersey

    S. Goldsterin

  2. Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    C. Kipnis

  3. Dipartimento di Matematica, Universita dell'Aquila, L'Aquila, Italy

    N. Ianiro

Authors
  1. S. Goldsterin
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  2. C. Kipnis
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  3. N. Ianiro
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Goldsterin, S., Kipnis, C. & Ianiro, N. Stationary states for a mechanical system with stochastic boundary conditions. J Stat Phys 41, 915–939 (1985). https://doi.org/10.1007/BF01010010

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  • DOI: https://doi.org/10.1007/BF01010010

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