  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.
