Precursory variations of Tsallis non-extensive statistical mechanics entropic index associated with the M9 Tohoku earthquake in 2011

Applying natural time analysis, which has been introduced by the authors in 2001, to the Japanese seismic data, we find that the system enters the critical stage upon the occurrence of M = 4.2–5.0 earthquakes from 08:36 to 13:14 local time (LT) on 10 March 2011, i.e., almost one day before the M 9 Tohoku earthquake on 11 March 2011. Here, we find that just before this period the Tsallis entropic index q of non-extensive statistical mechanics started to show distinct changes. In addition an evident change of q is found upon the occurrence of the M 7.3 foreshock at 11:45 LT on 9 March 2011, which exhibits a scaling behavior with a characteristic exponent 1∕3 that conforms to Lifshitz-Slyozov-Wagner theory for phase transitions.