Nonequilibrium physics meets time series analysis: Measuring probability currents from data

¹ Department of Physics, Chemnitz University of Technology D-09107 Chemnitz, Germany
² Max Planck Institute for the Physics of Complex Systems Nöthnitzer Str. 38, D-01187 Dresden, Germany

Corresponding authors: wolfram.just@physik.tu-chemnitz.de, kantz@mpipks-dresden.mpg.de

Received: 19 September 2002
Accepted: 24 January 2003

Abstract

We present a simple method to estimate probability currents of stochastic systems from a given time series. The method uses results of the theory of stochastic differential equations about conditional averages. Evaluation of the probability current directly aims at detecting the violation of detailed balance and hence yields the proper characterisation of nonequilibrium behaviour. We apply our approach to stochastic resonance and propose a novel resonance criterion which is based on the evaluation of the probability current. It agrees well with other measures, e.g. derived from correlations or signal-to-noise ratios. Finally, we demonstrate on an example of experimental wind data that our approach copes with real experimental data sets as well.