Long range correlations in stochastic transport with energy and momentum conservation

TL;DR

This paper studies a one-dimensional stochastic heat transport model conserving energy and momentum, revealing long-range correlations in the steady state and analyzing finite size effects and deviations from local equilibrium.

Contribution

It introduces a model with conserved quantities and explicitly computes long-range correlations and finite size corrections, advancing understanding of nonequilibrium steady states.

Findings

Model obeys Fourier law with finite heat conductivity.

Correlations are long ranged with explicit scaling forms.

Multi-lane variant shows correlations vanish, with deviations from local equilibrium quantified.

Abstract

We consider a simple one dimensional stochastic model of heat transport which locally conserves both energy and momentum and which is coupled to heat reservoirs with different temperatures at its two ends. The steady state is analyzed and the model is found to obey the Fourier law with finite heat conductivity. In the infinite length limit, the steady state is described locally by an equilibrium Gibbs state. However finite size corrections to this local equilibrium state are present. We analyze these finite size corrections by calculating the on-site fluctuations of the momentum and the two point correlation of the momentum and energy. These correlations are long ranged and have scaling forms which are computed explicitly. We also introduce a multi-lane variant of the model in which correlations vanish in the steady state. The deviation from local equilibrium in this model as expressed in terms of the on-site momentum fluctuations is calculated in the large length limit.