Nonextensive Statistical Mechanics

266 7 Thermodynamical and Nonthermodynamical ApplicationsFig. 7.59 The temperature dependences of (q, r)(a), and of (a q , a r ), used to fit the experimental dataof Fig. 7.58. Inset of (a): T -dependence of n(T ) ≡ 1/(q − 1) (from Fig. 15 of [283]) (from [282]).Summarizing, for both Mendeleev Table and doped fullerenes, the ground-statetotal energies (calculated respectively by ab-initio Hartree–Fock and FunctionalDensity Theory methods) are described (with all presently available precision) byone and the same equation, namely the q-exponential form (7.25)! The deep understandingof these two results constitutes, in our opinion, a fantastic challenge inthe chemical science. The derivation of the nontrivial index q = 0.58145 from firstprinciples would be more than expected. It would, among others, reveal whetherthere is a deep connection with nonextensivity, or whether it is just a coincidence.7.3 EconomicsA sensible amount of papers have used q-statistical concepts to discuss and/or extendvarious financial and economical quantities, such as distributions of returns,distributions of stock volumes, Black–Scholes equation, volatility “smile”, pricing,risk aversion in economic transactions, and various others [582–622].Some typical results are shown in Figs. 7.63, 7.64, 7.65, 7.66, 7.67, 7.68, 7.69,7.70, and 7.71.