Non-extensive statistics, fluctuations and correlations in high-energy nuclear collisions

Starting from the experimental evidence that high-energy nucleus-nucleus collisions cannot be described in terms of superpositions of elementary nucleon-nucleon interactions, we analyze the possibility that memory effects and long-range forces imply a non-extensive statistical regime during high-energy heavy-ion collisions. The relevance of these statistical effects and their compatibility with the available experimental data are discussed. In particular, we show that theoretical estimates obtained in the framework of the generalized non-extensive thermostatistics, can reproduce the shape of the pion transverse mass spectrum and explain the different physical origin of the transverse momentum correlation function of the pions emitted during the central Pb + Pb and during the p + p collisions at 158 GeV.