  Upon employing a natural time window of fixed length sliding through a time
series, an explicit interrelation between the variability $\beta$ of the
variance $\kappa_1$($=< \chi^2 > - < \chi >^2$) of natural time $\chi$ 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 $\beta$. 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 $\beta$
minima lower than the relative thresholds deduced from the fluctuation theorem,
thus signalling an impending major event.
