A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction

TL;DR

This paper investigates a symmetry property of momentum distribution functions in nonequilibrium steady states of lattice thermal conduction, highlighting how symmetry can be broken by asymmetric potentials or boundary conditions.

Contribution

It identifies a specific symmetry property of momentum distributions and explores how it is affected by asymmetries in interaction or boundary conditions.

Findings

Symmetry holds when equations of motion are symmetric.

Asymmetry introduced by potential or boundary conditions breaks the symmetry.

Numerical simulations show different behaviors with and without on-site potential.

Abstract

We study a symmetry property of momentum distribution functions in the steady state of heat conduction. When the equation of motion is symmetric under change of signs for all dynamical variables, the distribution function is also symmetric. This symmetry can be broken by introduction of an asymmetric term in the interaction potential or the on-site potential, or employing the thermal walls as heat reservoirs. We numerically find differences of behavior of the models with and without the on-site potential.