Does the non-extensivity parameter q capture the effect of long-range temporal correlations between the magnitudes of successive earthquakes?

Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process' memory and the process' increments infinite variance. By using also detrended fluctuation analysis for the detection of long-range temporal correlations, we study the existence of both temporal and magnitude correlations in real seismic data of California and Japan[NV Sarlis, ES Skordas and PA Varotsos, Phys. Rev. E 82, 021110 (2010)]. On the basis of natural time analysis, we investigate whether the nonextensivity parameter q can be considered as a measure of temporal organization of earthquakes.