From time series to superstatistics

TL;DR

This paper presents a method to derive superstatistical models from experimental time series, classifies data into three universality classes, and demonstrates the approach with turbulence data showing clear time scale separation.

Contribution

It introduces a systematic procedure to extract superstatistical parameters from time series and identifies three main universality classes for experimental data.

Findings

Velocity data in turbulent flow fits log-normal superstatistics

Two distinct superstatistical time scales are identified

Experimental data exhibit clear separation of time scales

Abstract

Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue that many experimental data fall into three different universality classes: chi^2-superstatistics (Tsallis statistics), inverse chi^2-superstatistics, and log-normal superstatistics. We discuss how to extract the two relevant well separated superstatistical time scales tau and T, the probability density of the superstatistical parameter beta, and the correlation function for beta from the experimental data. We illustrate our approach by applying it to velocity time series measured in turbulent Taylor-Couette flow, which is well described by log-normal superstatistics and exhibits clear time scale separation.