Thermodynamic properties and transport coefficients of QCD matter within the nonextensive Polyakov-Nambu-Jona-Lasinio model

Abstract

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the nonextensive statistical mechanics. This new statistics is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when q→1, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter q on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann (SB) limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities ϵT4, pT4, and sT3 all increase with q, exceed their usual SB limits, and tend to a new q-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of cs2 is still its SB limit 1/3. In addition, we found some similarities between the nonextensive effect and the finite-size effect. For example, as q increases (size decreases), the criticality of cvT3 and cs2 gradually disappears. Besides, in order to better study the nonextensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to q. And found that their response patterns are different.