Nonextensive Statistical Mechanics

7.2 Chemistry 259Fig. 7.49 (a) Dimensionless double well potential V (x) = ax 4 + bx 3 + cx 2 + d, witha =1/48, b =−1/9, c = 1/8, d = 3/16. The left (local) minimum occurs at x = x L = 0; theright (global) minimum occurs at x = x R = 3; the central maximum occurs at x = x 0 = 1. Thestationary distribution is shown for ρ = 2(b)andρ = 0.5(c), for typical values of D, as indicatedin the figure; q = 2 − ρ.Forq ≥ 1 the full phase-space is covered by power-law tails. For q < 1acutoff restricts the attainable space. Observe in (b) that, as D decreases, the motion becomes moreconfined until only the neighborhood of the deepest valley is allowed. The horizontal lines in (a)represent the cutoff condition V (x) = 1/β, which defines the allowed regions for q = 0andthesame values of D as in (b). All quantities are dimensionless (from [578]).7.2.2 Lattice Lotka–Volterra Model for Chemical Reactionsand GrowthThe lattice Lotka–Volterra (LLV) model is a paradigmatic one for two-constituentchemical reactions, growth, prey-predator, kinetics, and other phenomena. Its meanfieldapproximation (classical Lotka–Volterra model) is conservative, but its exactmicroscopic dynamics is not. A large literature is devoted to its study. Here we focuson the time dependence of its configurational entropy by following [579, 580]: seeFigs. 7.52, 7.53, 7.54, 7.55, 7.56, and 7.57, where the red and green colors indicate