Superstatistics: Recent developments and applications

TL;DR

This paper reviews recent advances in superstatistics, a framework for modeling nonequilibrium systems with fluctuating parameters, highlighting theoretical developments and diverse applications across physics and finance.

Contribution

It introduces new results on correlation functions and discusses recent applications, expanding the understanding of superstatistics in various fields.

Findings

Asymptotic decay of probability densities can be derived via a variational principle.

Correlation functions exhibit typical behaviors in dynamical superstatistical models.

Superstatistics has practical applications in hydrodynamics, astrophysics, and finance.

Abstract

We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic decay of stationary probability densities can be determined using a variational principle, and present some new results on the typical behaviour of correlation functions in dynamical superstatistical models. We briefly describe some recent applications of the superstatistics concept in hydrodynamics, astrophysics, and finance.