Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models

Gregory Eyink, Joel L. Lebowitz, Herbert Spohn

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57 Scopus citations


We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials. The unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non-reversible. We study the structure of the stationary measure in the hydrodynamic limit, as the microscopic lattice size goes to infinity. In particular, we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by Fick's law.

Original languageEnglish (US)
Pages (from-to)253-283
Number of pages31
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Aug 1990

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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