Nonextensive Statistical Mechanics

3.3 Correlations, Occupancy of Phase-Space, and Extensivity of S q 69like this that are addressed within the nonextensive scenario. 9 This remark maybe considered as some sort of golden reason for the present generalization of BGstatistical mechanics! 10(iii) If W eff (N) ∼ Cν N γ (N →∞) with C > 0 and ν>1 and 0 1, and 1/ρ ≥ 0). If 1/ρ = 0 we obtain W eff (N) ∼ Aμ N , i.e., case (i). If 1/ρ > 0we obtain W eff ( )(N) ∼ BN ρ with B ≡ A ln μ ρ,i.e., case (ii).ρ11 We might consider the following entropic functional: S γ = ∑ Wi=1 p i ln 1/γ (1/p i )(S 1 = S BG ),whose equal-probability expression is given by S γ = ln 1/γ W .IfweuseasW the expressionW eff (N) ∼ Cν N γ , we immediately verify that S γ (N) ∼ (ln 1/γ ν) N, hence extensive. It can bestraightforwardly verified that S γ ({p i }) is nonnegative, expansible, concave, and nonadditive.