Nonextensive Statistical Mechanics

48 3 Generalizing What We LearntFig. 3.8 Illustration of the dependence on (W, d)oftheratiosR q and Rq R for the entropies S q (left)and SqR (right), respectively. QC and QEP denote quasi-certainty and quasi-equal-probabilities(see the text). We see that lim d→0 lim W −1 →0 R q = 0 in all four cases, whereas it is violated for RqRfor the cases (QC, q < 1) and (QEP, q > 1). Not so for the two last cases, (QC, q > 1) and(QEP, q < 1), for which we do have lim d→0 lim W −1 →0 RqR = 0. The dashed (continuous) curvescorrespond to metric μ = 1(μ = 2) [110].