Nonextensive Statistical Mechanics

74 3 Generalizing What We Learnt10010090(a)90(b)8070q = 0.98070q = 0.96060S q5040q = 1.0S q5040q = 1.030302010q = 1.12010q = 1.10110203040506070809010001102030405060708090100NN20(c)S q10q = 0.9q = 1.0q = 1.1011020Fig. 3.14 S q (N)for(a) the Leibnitz triangle, (b) p = 1/2 independent subsystems, and (c) r N,0 =(1/2) N 1/2 . Only for q = 1wehaveafinite value for lim N→∞ S q (N)/N; itvanishes (diverges) forq > 1(q < 1). From [199].NTable 3.8 Restricted uniform distribution model with d = 1(top) andd = 2(bottom). Noticethat the number of triangle elements with nonzero probabilities grows like N, whereas that of zeroprobability grows like N 2(N = 0) (1, 1)(N = 1) (1, 1/2) (1, 1/2)(N = 2) (1, 1/3) (2, 1/3) (1, 0)(N = 3) (1, 1/4) (3, 1/4) (3, 0) (1, 0)(N = 4) (1, 1/5) (4, 1/5) (6, 0) (4, 0) (1, 0)(N = 0) (1, 1)(N = 1) (1, 1/2) (1, 1/2)(N = 2) (1, 1/4) (2, 1/4) (1, 1/4)(N = 3) (1, 1/7) (3, 1/7) (3, 1/7) (1, 0)(N = 4) (1, 1/11) (4, 1/11) (6, 1/11) (4, 0) (1, 0)