Superstatistical distributions from a maximum entropy principle

TL;DR

This paper introduces a maximum entropy approach to derive superstatistical distributions for complex nonequilibrium systems, providing a unified framework applicable to quantum, classical, and turbulent systems.

Contribution

It presents a novel maximum entropy principle for determining the distribution of fluctuating parameters in superstatistics, extending the theoretical foundation for analyzing complex systems.

Findings

Derived superstatistical distributions for quantum harmonic oscillator

Applied the method to classical ideal gas systems

Analyzed velocity time series in turbulent flow

Abstract

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter $\beta$ of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: The superstatistical quantum mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.