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

Abstract

We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\to 1$, 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 limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\frac{\epsilon }{T^4}$, $\frac{p}{T^4}$ and $\frac{s}{T^3}$ all increase with $q$, exceed their usual Stefan-Boltzmann 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 non-extensive 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 non-extensive 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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• Nonextensive statistical field theory
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model