A remarkable change of the entropy of seismicity in natural time under time reversal before the super-giant M9 Tohoku earthquake on 11 March 2011

Here, we analyze in natural time all earthquakes of magnitude ( M ) 3.5 or larger in Japan from 1 January 1984 until the occurrence of the super-giant M9 Tohoku earthquake on 11 March 2011. We find that two and a half months before this M9 earthquake a pronounced minimum of the entropy change of seismicity under time reversal is observed. Remarkably the exponent α resulting from the detrended fluctuation analysis of the earthquake magnitude time-series exhibits a simultaneous minimum with an unusual low value ( ) indicating an evident anticorrelated behavior. The validity of these findings is supported by the most studied non-conservative self-organized criticality model for earthquakes since it exhibts a non-zero change of the entropy upon time reversal, which reveals a breaking of the time symmetry, thus reflecting the predictability in this model.