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

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 dierential 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.