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From time series to superstatistics

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

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

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

Phys. Rev. E 72, 056133 – Published 29 November, 2005Erratum Phys. Rev. E 73, 049905 (2006)

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

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: $χ^{2}$ superstatistics (Tsallis statistics), inverse $χ^{2}$ 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.

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)

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From time series to superstatistics

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Erratum

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

Article Text

References (33)

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