Hierarchical maximum entropy principle for generalized superstatistical systems and Bose-Einstein condensation of light

TL;DR

This paper introduces a hierarchical entropy maximization principle for complex superstatistical systems with multiple dynamic levels, applied to photon Bose-Einstein condensates, offering an alternative to existing methods.

Contribution

It proposes a hierarchical entropy maximization framework for generalized superstatistics, extending the approach to systems with multiple dynamical levels and different underlying statistics.

Findings

Hierarchical entropy maximization reflects time-scale separation.

Applied to photon Bose-Einstein condensates in dye microcavities.

Provides an alternative to the master equation approach.

Abstract

A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of superstatistical subsystems, each made up of a set of cells, then the Boltzmann-Gibbs-Shannon entropy should be maximized first for each cell, second for each subsystem, and finally for the whole system. Hierarchical entropy maximization naturally reflects the sufficient time-scale separation between different dynamical levels and allows one to find the distribution of both the intensive parameter and the control parameter for the corresponding superstatistics. The hierarchical maximum entropy principle is applied to fluctuations of the photon Bose-Einstein condensate in a dye microcavity. This principle provides an alternative to the master equation approach recently applied to this problem. The possibility of constructing generalized superstatistics based on a statistics different from the Boltzmann-Gibbs statistics is pointed out.