Spatial correlations, additivity and fluctuations in conserved-mass transport processes

TL;DR

This paper derives exact two-point correlation functions for a broad class of conserved-mass transport processes, revealing their short-range correlations and equilibrium-like thermodynamic structure, including additivity and fluctuation-response relations.

Contribution

It provides the first exact calculation of spatial correlations in these processes and uncovers their thermodynamic properties in steady state.

Findings

Correlations are generally short-ranged.

Processes exhibit equilibrium-like additivity.

Subsystem mass distributions follow fluctuation-response relations.

Abstract

We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion and coalescence of masses. We find that the spatial correlations are in general short-ranged and consequently, on a large scale, these conserved-mass transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibriumlike additivity property, and a corresponding fluctuation-response relation, which helps us to obtain subsystem mass distributions in the limit of subsystem size large.