Correlations in Nonequilibrium Steady States

TL;DR

This paper investigates how energy correlations behave in nonequilibrium steady states of a 1-D model, revealing quadratic and linear scaling of covariances with system size and distance, respectively.

Contribution

It provides new insights into the scaling and spatial structure of energy covariances in nonequilibrium steady states through theoretical, conjectural, and numerical analysis.

Findings

Short-range covariances respond quadratically to temperature gradients.

Long-range covariances decay linearly with distance.

Results are consistent with known models like simple exclusion and KMP.

Abstract

We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how spatial covariances scale with system size, their relations to local thermodynamic quantities, and the randomizing effects of heat baths. Among our findings are that short-range covariances respond quadratically to local temperature gradients, and long-range covariances decay linearly with macroscopic distance. These findings are consistent with exact results for the simple exclusion and KMP models.