Gammalike mass distributions and mass fluctuations in conserved-mass transport processes

TL;DR

This paper demonstrates that in conserved-mass transport systems with short-range correlations, the steady-state mass distribution is uniquely determined by the variance-mean relationship, leading to a gamma distribution for subsystem masses.

Contribution

It establishes a general link between variance-mean dependence and the form of the steady-state distribution in conserved-mass transport models.

Findings

Variance of subsystem mass is proportional to the square of its mean.

Subsystem mass distribution is constrained to be a gamma distribution.

The result applies broadly to models with short-range correlations.

Abstract

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that joint mass distribution of subsystems is factorized in the thermodynamic limit. The factorization condition is not too restrictive as it would hold in systems with short-ranged spatial correlations. To demonstrate the result, we revisit a broad class of mass transport models and its generic variants, and show that the variance of subsystem mass in these models is proportional to square of its mean. This particular functional form of the variance constrains the subsystem mass distribution to be a gamma distribution irrespective of the dynamical rules.