Asymptotic Behavior of Thermal Non-Equilibrium Steady States for a Driven Chain of Anharmonic Oscillators

TL;DR

This paper analyzes the low-temperature asymptotic behavior of heat conduction in a nonlinear oscillator chain coupled to heat reservoirs, revealing a variational principle that characterizes the invariant measure and heat flow.

Contribution

It extends Freidlin-Wentzell theory to degenerate diffusions and establishes a variational characterization of the invariant measure at low temperatures.

Findings

Invariant measure characterized by a variational principle at low temperatures

Heat flow related to the variational principle

Extension of Freidlin-Wentzell theory to degenerate diffusions

Abstract

We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this limit, the invariant measure is characterized by a variational principle. We relate the heat flow to the variational principle. The main technical ingredient is an extension of Freidlin-Wentzell theory to a class of degenerate diffusions.