Nonextensive Statistical Mechanics

5.5 The q-Triplet 1910.500.48N = 20,000 - U = 0.69 (M 0 = 1)Single EventsEquilibrium0.46total calculation time for the CLT pdf = 200000Temperature0.440.42QSSevent 1 (of class 1)event 2 (of class 2)0.400.38event 3 (of class 3)10 1 10 2 10 3 10 4 10 5timeFig. 5.40 Time evolution of the temperature (calculated as twice the average kinetic energy perparticle) for three single events representative of the three different classes observed at U = 0.69for initial magnetization M 0 = 1. The size of the system is N = 20, 000 (from [46]).5.5 The q-TripletLet us further consider the ordinary differential equations that we addressed inSection 3.1.The solution of the differential equationis given bydydx= ay (y(0) = 1) (5.49)y = e ax . (5.50)We may heuristically think of it in three different physical manners, related respectivelyto the sensitivity to the initial conditions, to the relaxation in phase-space,and, if the system is Hamiltonian, to the distribution of energies at thermal equilibrium.In the first interpretation we reproduce Eq. (2.31). In the second interpretation,we focus some relaxing relevant quantity(t) ≡O(t) − O(∞)O(0) − O(∞) , (5.51)