Heat Conduction in a hard disc system with non-conserved momentum

TL;DR

This study uses computer simulations to analyze heat transport in a hard disc fluid with non-conserved momentum, showing that local thermodynamic equilibrium and Fourier's law hold in the large-system limit despite global fluctuations.

Contribution

It demonstrates that in a system with non-conserved momentum, local equilibrium and Fourier's law are valid in the thermodynamic limit, extending understanding of heat conduction in such models.

Findings

Profiles match local thermodynamic equilibrium in the limit

Fourier's law is obeyed in the large-system limit

Global fluctuations deviate from local equilibrium predictions

Abstract

We describe results of computer simulations of steady state heat transport in a fluid of hard discs undergoing both elastic interparticle collisions and velocity randomizing collisions which do not conserve momentum. The system consists of N discs of radius r in a unit square, periodic in the y-direction and having thermal walls at x = 0 with temperature T0 taking values from 1 to 20 and at x = 1 with T1 = 1. We consider different values of the ratio between randomizing and interparticle collision rates and extrapolate results from different N, to N->infinity, r->0 such that rho=1/2. We find that in the (extrapolated) limit N->infinity, the systems local density and temperature profiles are those of local thermodynamic equilibrium (LTE) and obey Fourier's law. The variance of global quantities, such as the total energy, deviates from its local equilibrium value in a form consistent with macroscopic fluctuation theory.