Non-extensive NJL model study of QCD phase structure with chiral imbalance and strong magnetic fields

Based on the two-flavor NJL model with Tsallis non-extensive statistics, this work explores the QCD phase structure and thermodynamic properties under strong magnetic fields and chiral imbalance. The Tsallis parameter $q$ captures non-equilibrium effects relevant to heavy-ion collisions. Key findings reveal that the critical temperature $T_c$ decreases with increasing $q$, indicating that non-equilibrium conditions promote chiral symmetry restoration at lower temperatures. The chiral chemical potential $\mu_5$ significantly alters the magnetic response, with a transition from magnetic catalysis to inverse magnetic catalysis under certain conditions. For $q > 1$, non-monotonic behavior of $T_c$ with magnetic field $eB$ emerges. Pressure becomes anisotropic under strong $eB$, and the speed of sound exhibits a dip near $T_c$, shifting to lower temperatures with larger $q$. These results highlight how non-extensive statistics, chiral imbalance, and magnetic fields collectively influence the QCD phase diagram and thermodynamic observables, offering insights for interpreting heavy-ion collision data.