Nonextensive Statistical Mechanics

128 4 Stochastic Dynamical Foundations of Nonextensive Statistical MechanicsFig. 4.10 TMNT model with ρ = 0.5. Top: Distributions of the sum of N random variables forincreasingly large values of N, and their fittings with q-Gaussians (continuous curves). Bottom:Influence of N on the fitting value of q. These results provide numerical support to the relation(4.56).statistical mechanics. Indeed, for ρ = 0 (independent variables) we obtain q = 1,whereas, for ρ ≠ 0(d = 1 system of correlated variables with periodic boundaryconditions), we obtain q = 1forα>1(short-range correlations) and q ≠ 1for0