Nonextensive Statistical Mechanics

200 5 Deterministic Dynamical Foundations of Nonextensive Statistical MechanicsFig. 5.53 Normalized two-time auto-correlation function of the state variable (θ, p) vs. time, foru = 0.69 (subcritical) and for initial conditions that guarantee that the system will get trappedinto a quasi stationary trajectory. Data correspond to averages over 200 of such trajectories. Thewaiting times are t w = 8 × 4 n , with n = 0,...,6. The dependence of C on both times is evident(from [44]).Fig. 5.54 Auto-correlation function vs. scaled time. The data are the same shown in Fig. 5.53 forthe three largest t w , but suitably scaling the time coordinate makes the data collapse into a single−0.2t/t 0.9Wcurve. The red solid line corresponds to e2.35 . Inset: ln q -linear representation of the same data,with q = 2.35. Linearity indicates q-exponential behavior (from [44]).