Following the basic prescriptions of the Tsallis' nonextensive relativistic thermodynamics, we investigate the relevance of nonextensive statistical effects on the relativistic nuclear and subnuclear equation of state. In this framework, we study the first order phase transition from hadronic to quark-gluon plasma phase by requiring the Gibbs conditions on the global conservation of the electric and the baryon charges. The relevance of small deviations from the standard extensive statistics is investigated in the context of intermediate and high energy heavy-ion collisions.

Experimental measurements in terrestrial laboratory, space and astrophysical observations of variation and fluctuation of nuclear decay constants, measurements of large enhancements in fusion reaction rate of deuterons implanted in metals and electron capture by nuclei in solar core indicate that these processes depend on the environment where they take place and possibly also on the fluctuation of some extensive parameters and eventually on stellar energy production. Electron screening is the first important environment effect. We need to develop a treatment beyond the Debye-Hückel screening approach, commonly adopted within global thermodynamic equilibrium. Advances in the description of these processes can be obtained by means of q-thermostatistics and/or superstatistics for metastable states. This implies to handle, without ambiguities, the case q < 1.

Galitskii and Yakimets showed that in dense or low temperature plasma, due to quantum uncertainty effect, the particle distribution function over momenta acquires a power-like tail even under conditions of thermodynamic equilibrium. We show that in weakly non-ideal plasmas, like the solar interior, both non-extensivity and quantum uncertainty should be taken into account to derive equilibrium ion distribution functions and to estimate nuclear reaction rates and solar neutrino fluxes. The order of magnitude of the deviation from the standard Maxwell-Boltzmann distribution can be derived microscopically by considering the presence of random electrical microfield in the stellar plasma. We show that such a nonextensive statistical effect can be very relevant in many nuclear astrophysical problems.

The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the importance of the velocity distribution of ions. Then the properties (density and temperature) of the weak-coupled solar plasma are analysed, showing that the ion velocities should deviate from the Maxwellian distribution and could be better described by a weakly-nonextensive (|q-1| < 0.02) Tsallis' distribution. We discuss concrete physical frameworks for calculating this deviation: the introduction of higher-order corrections to the diffusion and friction coefficients in the Fokker-Planck equation, the influence of the electric-microfield stochastic distribution on the particle dynamics, a velocity correlation function with long-time memory arising from the coupling of the collective and individual degrees of freedom. Finally, we study the effects of such deviations on stellar nuclear rates, on the solar neutrino fluxes, and on the pp neutrino energy spectrum, and analyse the consequences for the solar neutrino problem.