Nonextensive Statistical Mechanics

170 5 Deterministic Dynamical Foundations of Nonextensive Statistical MechanicsFig. 5.19 Time evolution of the q-entropy for the non-dissipative baker map, using 16 digit calculations.Top: S q (t) for entropic indices q = 0.80, 0.85, 0.90, 0.95, 1.00, 1.05, 1.10, 1.15, 1.20 (fromtoptobottom)whenW = 10 4 and N = 10 6 . Bottom: S 1 (t) for typical values of W (W = 10 4 ,4 × 10 4 ,16× 10 4 ; N = 10W ). Notice that the bounding value for the q = 1 entropy corresponds,in all cases, to equiprobability, i.e., ln W . The slope dS 1 (t)/dt (on the left side) recoversthe well-known values for the Lyapunov exponents λ (1)1=−λ (2)1= ln 2 (from [138]).