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

Starting from the experimental evidence that high-energy nucleus-nucleus co llisions cannot be described in terms of superpositions of elementary nucle on-nucleon interactions, we analyze the possibility that memory effects and long-range forces imply a non-extensive statistical regime during high-ene rgy heavy-ion collisions. The relevance of these statistical effects and th eir compatibility with the available experimental data are discussed. In pa rticular, we show that theoretical estimates obtained in the framework of t he generalized non-extensive thermostatistics, can reproduce the shape of t he 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.