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

Abstract 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 $$T_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> decreases with increasing q , indicating that non-equilibrium conditions promote chiral symmetry restoration at lower temperatures. The chiral chemical potential $$\mu _5 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>μ</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:math> significantly alters the magnetic response, with a transition from magnetic catalysis to inverse magnetic catalysis under certain conditions. For $$q &gt; 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , non-monotonic behavior of $$T_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> with magnetic field eB emerges. Pressure becomes anisotropic under strong eB , and the speed of sound exhibits a dip near $$T_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , 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.