The transverse momentum (p T ) spectra from heavy-ion collisions at intermediate momenta are described by non-extensive statistical models. Assuming a fixed relative variance of the temperature fluctuating event by event or alternatively a fixed mean multiplicity in a negative binomial distribution (NBD), two different linear relations emerge between the temperature, T , and the Tsallis parameter q − 1. Our results qualitatively agree with that of G. Wilk. Furthermore we revisit the "Soft+Hard" model, proposed recently by G. G. Barnaföldi et.al., by a T -independent average p 2 T assumption. Finally we compare results with those predicted by another deformed distribution, using Kaniadakis' κ parametrization.

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature and baryon chemical potential in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis' statistics, is characterized by a dimensionless nonextensive parameter, , and the results in the usual Boltzmann-Gibbs case are recovered when → 1. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature is shown to decrease with increasing from the phase diagram in the ( , ) plane. However, larger values of cause the rise of at low temperature but high chemical potential. Moreover, it is found that different from zero corresponds to a first-order phase transition while = 0 to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with increasing due to the nonextensive effects.

Based on Tsallis entropy [1] and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while [3,4]. However, aiming at a non-extensive quantum statistics further requirements arise from the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or "cut and paste" solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the κand q-exponential behave in this respect.

The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' q−average of physical quantities, the sum p q j , is independent of the probability p i for Tsallis parameter q. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the q-deformed Bose-Einstein distribution as well as the q-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized q-distribution functions discussed in literature.

We analyze the connection between pT and multiplicity distributions in a statistical framework. We connect the Tsallis parameters, T and q, to physical properties like average energy per particle and the second scaled factorial moment, F2 = n(n − 1) / n 2 , measured in multiplicity distributions. Near and far from equilibrium scenarios with master equations for the probability of having n particles, Pn, are reviewed based on hadronization transition rates, µn, from n to n + 1 particles.