Nonextensive Statistical Mechanics

7.1 Physics 245Fig. 7.30 Log–Log plots of the cumulative distribution of calm-times in California (top) andJapan (bottom). Dots from the California and Japan catalogs, respectively; continuous curvesfrom Eq. (7.14). Insets: The same in q-log vs. linear representation (California: q = 1.13,τ 0 = 1724 s, and the linear regression coefficient R =−0.988; Japan: q = 1.05, τ 0 = 1587 s, andR =−0.990). For details see [544].ConsequentlywithdP(> r)p(r) =− = 1 e −r/[r 0(2−Q)]Q, (7.12)dr r 0Q ≡ 2 − 1 q < q . (7.13)Let us address now a different phenomenon, namely the fact that, between successiveearthquakes in a given area of the globe, there are calm-times, noted τ, anddefined through a fixed threshold m th for the magnitude. It has been verified [544]that, in California and Japan, the calm-time distribution, p(τ), happens to be wellrepresented (see Fig. 7.30) by a q-exponential form. More precisely, the correspondingaccumulated probability is given by the Abe–Suzuki time lawP(> τ) = e −τ/τ 0q (q > 1; τ 0 > 0) . (7.14)