A classification of nonequilibrium steady states based on temperature correlations

TL;DR

This paper introduces a new classification scheme for nonequilibrium steady states in statistical mechanics based on temperature correlations, expanding the understanding of generalized ensembles like superstatistics and Tsallis' statistics.

Contribution

It proposes a novel classification of generalized ensembles using the inverse temperature covariance parameter, unifying supercanonical and subcanonical states.

Findings

The inverse temperature covariance parameter is non-negative in superstatistics.

The parameter can be negative in other ensemble families.

Examples of supercanonical and subcanonical states are provided.

Abstract

Although generalized ensembles have now been in use in statistical mechanics for decades, including frameworks such as Tsallis' nonextensive statistics and superstatistics, a classification of these generalized ensembles outlining the boundaries of validity of different families of models, is still lacking. In this work, such a classification is proposed in terms of supercanonical and subcanonical ensembles, according to a newly defined parameter, the inverse temperature covariance parameter $\mathcal{U}$. This parameter is non-negative in superstatistics (and is equal to the variance of the inverse temperature) but can be negative for other families of statistical ensembles, adquiring then a broader meaning. It is shown that $\mathcal{U}$ is equal for every region of a composite system in a steady state, and examples are given of supercanonical and subcanonical states.