From time series to superstatistics.
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: Chi2 superstatistics (Tsallis statistics), Chi2 inverse 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.
Beck
Christian
C
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom.
Cohen
Ezechiel G D
EG
Swinney
Harry L
HL