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Fluctuation theorem and natural time analysis

Upon employing a natural time window of fixed length sliding through a time series, an explicit interrelation between the variability $β$ of the variance $κ_1$($=< χ^2 > - < χ>^2$) of natural time $χ$ and events' correlations is obtained. In addition, we investigate the application of the fluctuation theorem, which is a general result for systems far from equilibrium, to the variability $β$. We consider for example, major earthquakes that are nonequilibrium critical phenomena. We find that four (out of five) mainshocks in California during 1979-2003 were preceded by $β$ minima lower than the relative thresholds deduced from the fluctuation theorem, thus signalling an impending major event.