Local Thermal Equilibrium for Certain Stochastic Models of Heat Transport

Yao Li, Péter Nándori, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their “local environments” rather than directly with one another. The physical domain of the system can be a bounded region of (Formula presented.) for any (Formula presented.). We assume that the temperature at the boundary of the domain is prescribed and is nonconstant, so that the system is forced out of equilibrium. Our main result is local thermal equilibrium in the infinite volume limit. In the Hamiltonian context, this would mean that at any location x in the domain, local marginal distributions of NESS tend to a probability with density (Formula presented.) , permitting one to define the local temperature at x to be (Formula presented.). We prove also that in the infinite volume limit, the mean energy profile of NESS satisfies Laplace’s equation for the prescribed boundary condition. Our method of proof is duality: by reversing the sample paths of particle movements, we convert the problem of studying local marginal energy distributions at x to that of joint hitting distributions of certain random walks starting from x, and prove that the walks in question become increasingly independent as system size tends to infinity.

Original languageEnglish (US)
Pages (from-to)61-91
Number of pages31
JournalJournal of Statistical Physics
Volume163
Issue number1
DOIs
StatePublished - Apr 1 2016

Fingerprint

Heat Transport
Local Equilibrium
Thermal Equilibrium
Nonequilibrium Steady State
Stochastic Model
heat
Marginal Distribution
Tend
Laplace equation
reversing
Energy Distribution
Sample Path
Laplace's equation
Energy
random walk
Walk
infinity
Convert
Random walk
energy distribution

Keywords

  • Heat transport
  • Local thermodynamic equilibrium
  • Nonequilibrium steady states

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Local Thermal Equilibrium for Certain Stochastic Models of Heat Transport. / Li, Yao; Nándori, Péter; Young, Lai-Sang.

In: Journal of Statistical Physics, Vol. 163, No. 1, 01.04.2016, p. 61-91.

Research output: Contribution to journalArticle

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