Asymptotics of superstatistics

TL;DR

This paper develops a saddle-point approximation technique to analyze the large energy asymptotics of stationary distributions in superstatistics, encompassing Tsallis statistics as a special case, with detailed examples.

Contribution

It introduces a novel saddle-point method for asymptotic analysis of superstatistics, linking it to a variational principle and broadening understanding of nonequilibrium systems.

Findings

The technique effectively analyzes large energy asymptotics.

Superstatistics include Tsallis statistics as a special case.

Several detailed examples demonstrate the method's applicability.

Abstract

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special case. We develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics. A saddle-point approximation is developed which relates this problem to a variational principle. Several examples are worked out in detail.