Nonextensive Statistical Mechanics

5.7 A Conjecture on the Time and Size Dependences of Entropy 201Fig. 5.55 Auto-correlation function vs. time for u = 5 (supercritical) for N = 1000 and variousvalues of t W . The data correspond to an average over 10 trajectories initialized with water-bagconfiguration. Notice that, as in standard BG systems at thermal equilibrium, there is no aging.Inset: Semilog representation of the same data (from [379]).Fig. 5.56 Histogram of normalized angles at different times of the HMF dynamics. Parameters andinitial conditions are the same used in previous figures. Notice that at long times, the histogram isof the q-Gaussian form. Inset: squared deviation as a function of time. It follows the law σ 2 ∼ t γ ,with γ>1, signaling superdiffusion (from [44]).