Non-Equilibrium Steady States and Transport in the Classical Lattice $\phi ^4$ Theory

TL;DR

This paper investigates non-equilibrium steady states and thermal transport in classical lattice $\,\phi^4$ theory, analyzing thermal conductivity, linear response validity, and the transition from local equilibrium to non-equilibrium.

Contribution

It provides a detailed analysis of steady states, thermal conductivity, and the applicability of linear response theory in classical lattice scalar field theory.

Findings

Linear response theory applies under moderate thermal gradients.

Thermal conductivity depends on temperature and is computed explicitly.

Transition from local equilibrium to non-equilibrium is characterized.

Abstract

We study the classical non-equilibrium statistical mechanics of scalar field theory on the lattice. Steady states are analyzed near and far from equilibrium. The bulk thermal conductivity is computed, including its temperature dependence. We examine the validity of linear response predictions, as well as properties of the non-equilibrium steady state. We find that the linear response theory applies to visibly curved temperature profiles as long as the thermal gradients are not too strong. We also examine the transition from local equilibrium to local non-equilibrium.