Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU (3) quark mean field model

Abstract

In the present work, we apply Tsallis non-extensive statistics to study the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3) quark mean field model. Within this model, the properties of the quark matter are modified through the scalar fields $\sigma, \zeta, \delta, \chi$, the vector fields $\omega, \rho$, $\phi$, and the Polyakov fields $\Phi$ and $\bar{\Phi}$ at finite temperature and chemical potential. Non-extensive effects have been introduced through a dimensionless parameter $q$ and the results are compared to the extensive case ($q\rightarrow1$). In the non-extensive case, the exponential in the Fermi-Dirac (FD) function is modified to a $q$-exponential form. The influence of $q$ parameter on the thermodynamic properties: pressure, energy, and entropy density as well as trace anomaly is investigated. The speed of sound and specific heat with non-extensive effects is also studied. Furthermore, the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of $u, d,$ and $s$ quarks is explored. We found that the critical end point (CEP), which defines the point in the $(T - \mu)$ phase diagram where the order of the phase transition changes, shifts to a lower value of temperature, $T_{CEP}$, and a higher value of chemical potential, $\mu_{CEP}$, as the non-extensivity is increased, i.e., $q>$1.