Correlations in superstatistical systems

TL;DR

This paper reviews higher-dimensional superstatistical models, analyzing a 3D turbulence example, and demonstrates excellent agreement with experimental data across various statistical measures, advancing understanding of superstatistical systems.

Contribution

It provides a detailed analysis of superstatistical models in higher dimensions, specifically applying to 3D turbulence and comparing with experimental data, highlighting their predictive accuracy.

Findings

Excellent agreement with experimental data on turbulence statistics

Validation of superstatistical models for acceleration densities and correlations

Insights into transitioning from superstatistics to thermodynamics

Abstract

We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental data. Excellent agreement is obtained for various measured quantities, such as acceleration probability densities, Lagrangian scaling exponents, correlations between acceleration components, and time decay of correlations. We comment on how to proceed from superstatistics to a thermodynamic description.