Nonextensive Statistical Mechanics

3.3 Correlations, Occupancy of Phase-Space, and Extensivity of S q 77{1 (N−n)! n!N,n = + l (d,ɛ)N+1 N! N,ns(d) N(n ≤ d)0 (n > d) , (3.139)r (d,ɛ)where the excess probability s (d)Nand the distribution ratio l(d,ɛ)N,n(with 0 1.ThesystemisassumedatT = 0, hence it is in its ground state (assumed nondegenerate due to the presence of a vanishing external field within the easy magnetizationplane). Since it is in a pure state, its density matrix ρ N satisfies Trρ 2 N = 1.Consequently, the entropy S q (N) = 0, ∀q > 0. If we focus, however, on a block ofL elements with L < N, and define ρ L ≡ Tr N−L ρ N (Tr N−L denotes that we are