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

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 $q\ensuremath{\rightarrow}1$, 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 $\frac{\ensuremath{\epsilon}}{{T}^{4}}$, $\frac{p}{{T}^{4}}$, and $\frac{s}{{T}^{3}}$ 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 ${c}_{s}^{2}$ 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 $\frac{{c}_{v}}{{T}^{3}}$ and ${c}_{s}^{2}$ 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.

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