Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction

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Abstract

This paper contains rigorous results for a simple stochastic model of heat conduction similar to the KMP (Knipnis-Marchiori-Presutti) model but with possibly energy-dependent interaction rates. We prove the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, and exponential convergence to steady states from suitable initial conditions.

Original languageEnglish (US)
Pages (from-to)1170-1193
Number of pages24
JournalJournal of Statistical Physics
Volume152
Issue number6
DOIs
StatePublished - Sep 2013

Keywords

  • Energy exchange
  • Markov chains
  • Nonequilibrium steady states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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