Additivity property and emergence of power laws in nonequilibrium steady states

TL;DR

This paper demonstrates that an equilibriumlike additivity property can explain the emergence of power-law distributions in nonequilibrium steady states, providing a way to determine their scaling forms and exponents.

Contribution

It reveals that additivity can lead to power-law distributions in nonequilibrium systems and calculates subsystem mass distributions using this property across various models.

Findings

Power-law distributions arise from additivity in nonequilibrium states.

The full distribution form and exponents are determined by the additivity property.

Asymptotic behavior is governed by branch-cut singularity in variance.

Abstract

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.