Power-law quantum distributions in protoneutron stars

We investigate the bulk properties of protoneutron stars in the framework of a relativistic mean field theory based on nonextensive statistical mechanics, originally proposed by C. Tsallis and characterized by power-law quantum distributions. We study the relevance of nonextensive statistical effects on the β-stable equation of state at fixed entropy per baryon, for nucleonic and hyperonic matter. We concentrate our analysis in the maximum heating and entropy per baryon s = 2 stage and T ≈ 40 ÷ 80 MeV. This is the phase, at high temperature and high baryon density, in which the presence of nonextensive effects may alter more sensibly the thermodynamical and mechanical properties of the protoneutron star. We show that nonextensive power-law effects could play a crucial role in the structure and in the evolution of the protoneutron stars also for small deviations from the standard Boltzmann-Gibbs statistics.