Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

Sheldon Katz, Joel L. Lebowitz, Herbert Spohn

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We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external field E. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibrium E=0. At low temperatures and large E the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value at E=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.

Original languageEnglish
Pages (from-to)497-537
Number of pages41
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Feb 1984
Externally publishedYes


  • Steady states
  • fast ionic conductors
  • stochastic lattice gas models


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