Nonextensive Statistical Mechanics

7.1 Physics 227Fig. 7.6 The dashed and continuous straight lines correspond to a phenomenological q-statisticalapproach with q = 1andq = 1.114, respectively. The dots have been obtained from a quantumcalculation (from [421]).7.1.2.4 Diffusion of Charm QuarkA preliminary analysis of the diffusion of a charm quark in a thermal quark-gluonplasma is available [421]. A direct quantum mechanical calculation and a phenomenologicaltheory based on q-statistics are compared in Fig. 7.6. The two calculationsroughly coincide for q = 1.114, whereas the discrepancy is considerableif q = 1 is adopted instead. Further microscopic dynamical (and surely nontrivial!)studies are certainly necessary in order to understand why the specific valueq = 1.114 provides a good first approximation, and why, even for this value, asmall but visible systematic discrepancy is observed.As one more admissible application in the area of high-energy physics, let usmention that a detailed literature exists advancing a possible connection betweenthe solar neutrino problem and nonextensive statistics. Indeed, by now the wellestablishedneutrino oscillations do not totally explain, in some cases, the discrepancyexist’s between the theoretical predictions based on the Standard Solar Modeland the neutrino fluxes measured on Earth. Therefore, some other contributionsmight be there. It is proposed [422–424] that they come from the fact that mostprobably the solar plasma is not in thermal equilibrium, but in a kind of stationarystate instead, where nonextensive phenomena (basically due to strong spatialtemporalcorrelations) could be present and relevant.7.1.3 TurbulenceQuite an effort has been dedicated to understanding the ubiquitous connectionsof nonextensive statistics with turbulence. This includes lattice-Boltzmann models[425, 426], defect turbulence [427], rotations in oceanic flows [428], air turbulence