From time series to superstatistics

Christian Beck, Ezechiel G. D. Cohen, and Harry L. Swinney
Phys. Rev. E 72, 056133 – Published 29 November 2005; Erratum Phys. Rev. E 73, 049905 (2006)

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: χ2 superstatistics (Tsallis statistics), inverse χ2 superstatistics, and log-normal superstatistics. We discuss how to extract the two relevant well separated superstatistical time scales τ and T, the probability density of the superstatistical parameter β, and the correlation function for β 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.

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  • Received 18 July 2005

DOI:https://doi.org/10.1103/PhysRevE.72.056133

©2005 American Physical Society

Erratum

Erratum: From time series to superstatistics [Phys. Rev. E 72, 056133 (2005)]

Christian Beck, Ezechiel G. D. Cohen, and Harry L. Swinney
Phys. Rev. E 73, 049905 (2006)

Authors & Affiliations

Christian Beck

  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

Ezechiel G. D. Cohen

  • The Rockefeller University, 1230 York Avenue, New York, New York 10021, USA

Harry L. Swinney

  • Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA

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Issue

Vol. 72, Iss. 5 — November 2005

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