Nonextensive Statistical Mechanics

7.1 Physics 2551.25fit in Fig.2Eq.(13)1.2q1.1510 0.2Eq.(11)Eq.(12)1.1K r/K L10 0.1 δ = 0.1110 –2 10 –1 10 01.05Δt L = 48 daysΔt/Δt LSOI; Jan 1999 − Sept 2006110 −3 10 −2 10 −110 0Δt /Δt LFig. 7.44 Dependence of q on the (conveniently rescaled) time lag for the SOI. The data correspondto the Jan 1999–Sept 2006 period. See [293] for further details.function be replaced by a q-exponential form. This conjecture has indeed been verifiednumerically [546, 547], as can be seen in Figs. 7.45, 7.46, and 7.47.7.1.11 Quantum EntanglementA considerable effort has been dedicated to the connections between generalizedentropic forms and the location of the critical frontier which has separable states onone side and quantum entangled ones on the other one. A remarkably simple, andsometimes quite performant, criterium based on the conditional form of the entropyS q was advanced by Abe and Rajagopal in [548]. For some systems, this procedureenabled the exact calculation of the separable-entangled separatrix. Such is the caseillustrated in Fig. 7.48 (from [549]). An entire literature exists in fact exploring thisand related questions [114, 550–571].7.1.12 Random MatricesThe standard Gaussian ensembles of random matrices can be alternatively obtainedby maximizing the Boltzmann–Gibbs–von Neumann entropy under appropriateconstraints. By optimizing instead the entropy S q it is possible to q-generalize such