Nonextensive Statistical Mechanics

5.7 A Conjecture on the Time and Size Dependences of Entropy 203Fig. 5.59 The same as in Fig. 5.58 but with a N-scaled time axis. From [285].Fig. 5.60 (a) Time evolution of the HMF velocity autocorrelation functions for U = 0.69, N =1000, and different initial conditions are nicely reproduced by q-exponential curves. The entropicindex q used is also reported. (b) Time evolution of the variance of the angular displacementfor U = 0.69, N = 2000, and different initial conditions. After an initial ballistic motion, theslope indicates a superdiffusive behavior with an exponent γ greater than 1. This exponent is alsoreported and indicated by dashed straight lines. Anomalous diffusion does not depend in a sensitiveway on the size of the system. For both the plots shown, the numerical simulations are averagedover many realizations (from [41]).