Nonextensive Statistical Mechanics

262 7 Thermodynamical and Nonthermodynamical ApplicationsFig. 7.54 Time evolution for initial conditions very localized within a L-sizedstripinaL × Lsquare lattice (from [579]).the two constituents, and the white color indicates that the cell is empty. The entropyS q of the D-dimensional model with very localized initial conditions asymptoticallyincreases linearly with time only forq = 1 − 1 D . (7.22)This is, essentially, a kind of trivial consequence of the fact that the number W ofpossibilities increases as the available D-dimensional hypervolume, i.e., W ∝ t D .Consequently, if we consider the simplest case, namely equal probabilities, S q =ln q W ∼ W 1−q /(1 − q) ∝ t (1−q)D . Then, in order to have S q ∝ t, Eq. (7.22) mustbe satisfied. This equation is, in fact, but the particular case of Eq. (3.120) withρ = D. Let us also note that the possibly nontrivial entropic effects associated