Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model

The influence of non-extensive Tsallis statistics on the hadron phase structure has been investigated using the Polyakov-quark-meson (PQM) model. The analysis examines the non-extensive effects on the temperature dependence of PQM order parameters, thermodynamic quantities related to the QCD equation of state, and fluctuations of conserved charges at varying chemical potentials. The results show that non-extensive effects have the most significant deviations near the crossover region. The pseudo-critical temperature $T_{\chi }({\mu }_B)$ is not a universal constant and decreases with increasing non-extensive $q$ parameter. The chiral phase diagram of the PQM model indicates a decrease in the behavior of the ($T_{\chi }-{\mu }_B$) plane with increasing non-extensive $q$ parameter. The PQM model exhibits good qualitative agreement with lattice QCD calculations. Moreover, these findings suggest the existence of a Tsallis limit, which serves as an alternative to the Stefan-Boltzmann (SB) limit for the massless ideal gas. The critical endpoint (CEP) exhibits lower temperature but higher chemical potential with increasing non-extensive $q$ parameter. Overall, this study highlights the importance of non-extensive Tsallis statistics in characterizing the quark-hadron phase structure of the PQM model and contributes to a deeper understanding of non-extensive effects in the quark-hadron phase transition.