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

Yao Li; Lai Sang Young

doi:10.1007/s10955-013-0801-1

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

Yao Li, Lai Sang Young

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1170-1193
Number of pages	24
Journal	Journal of Statistical Physics
Volume	152
Issue number	6
DOIs	https://doi.org/10.1007/s10955-013-0801-1
State	Published - Sep 2013

Keywords

Energy exchange
Markov chains
Nonequilibrium steady states

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-013-0801-1

Cite this

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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.",

keywords = "Energy exchange, Markov chains, Nonequilibrium steady states",

author = "Yao Li and Young, {Lai Sang}",

note = "Funding Information: LSY was supported in part by NSF Grant DMS-1101594.",

year = "2013",

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doi = "10.1007/s10955-013-0801-1",

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AB - 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.

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KW - Markov chains

KW - Nonequilibrium steady states

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

Abstract

Keywords

ASJC Scopus subject areas

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