The QCD phase diagram of the SU(2) NJL model with chiral chemical potential under a non-extensive framework

Abstract This article investigates the thermodynamic properties of the SU(2) Nambu–Jona–Lasinio (NJL) model under 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> , employing Tsallis non-extensive statistics. The introduction of the parameter $$ q $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> , which characterizes the non-extensivity of the system through Tsallis statistics, offers a novel perspective for studying the behavior of strongly interacting matter under extreme conditions. By calculating thermodynamic quantities such as quark mass, critical temperature, chiral density, pressure, entropy, and speed of sound, we systematically analyze the effects of $$ \mu _5 $$ <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> and $$ q $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> on these quantities. It is observed that both $$ \mu _5 $$ <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> and $$ q $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> exhibit an inverse relationship with the critical temperature $$ T_\textrm{pc} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>pc</mml:mtext> </mml:msub> </mml:math> , while showing a positive correlation with the chiral density $$\left\langle n_{5}\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:mfenced> </mml:math> .