Classical and quantum non-extensive statistics effects in nuclear many-body problems

Recent progress in statistical mechanics indicates the Tsallis non-extensive thermostatistics as the natural generalization of the standard classical and quantum statistics, when memory effects and long-range forces are not negligible. In this framework, we show that in weakly non-ideal plasma non-extensive and quantum uncertainty effects should be taken into account to derive the equilibrium distribution functions, quantum fluctuations and correlations between the particles. The strong influence of these effects is discussed in the context of the solar neutrino problem and in the high-energy nuclear–nuclear collision experiments. Although the deviation from the Boltzmann–Gibbs statistics, in both cases, is very small, the nuclear reaction rates and quantum fluctuations are strongly influenced by the non-extensive feature of the solar plasma and the hadronic gas produced by a quark–gluon plasma. The discrepancies between the experimental data and theoretical previsions are sensibly reduced.