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Lattice gas models in contact with stochastic reservoirs: Local equilibrium and relaxation to the steady state

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Abstract

Extending the results of a previous work, we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. We establish here the local equilibrium structure of the stationary measures for these models. Further, we prove as a law of large numbers that the time-dependent empirical density field converges to a deterministic limit process which is the solution of the initial-boundary value problem for a nonlinear diffusion equation.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Rutgers University, 08903, New Brunswick, NJ, USA

    Gregory Eyink & Joel L. Lebowitz

  2. Theoretische Physik, Universität München, W-8000, München, Federal Republic of Germany

    Gregory Eyink & Herbert Spohn

Authors
  1. Gregory Eyink
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  2. Joel L. Lebowitz
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  3. Herbert Spohn
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Additional information

Communicated by A. Jaffe

Supported in part by NSF Grants DMR89-18903 and INT85-21407. G.E. and H.S. also supported by the Deutsche Forschungsgemeinschaft

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Eyink, G., Lebowitz, J.L. & Spohn, H. Lattice gas models in contact with stochastic reservoirs: Local equilibrium and relaxation to the steady state. Commun.Math. Phys. 140, 119–131 (1991). https://doi.org/10.1007/BF02099293

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  • DOI: https://doi.org/10.1007/BF02099293

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