Nonextensive Statistical Mechanics

40 3 Generalizing What We Learnt1e q–xq = 20.1q = 10.01q = –1q = 00 1 2 3 x 4Fig. 3.3 The q-exponential function eq−x for typical values of q: log–linear scales. It is convex(concave) if q > 1(q < 1). For q < 1, it has a vertical asymptote at x = (1 − q) −1 .0.01 0.1 1 10 x 1001e –x q0.1q = 20.01q = –1q = 0 q = 1Fig. 3.4 The q-exponential function eq−x for typical values of q: log–log scales. For q > 1, it hasan asymptotic slope equal to −1/(q − 1).