Lesser Green's Function and Chirality-Reduced Entropy via the In-Medium NJL Model

Abstract

We investigate chiral symmetry restoration in hot and dense quark matter using a correlator-based chirality-reduced entropy in the in-medium Nambu--Jona-Lasinio (NJL) model. Starting from the lesser Green's function $G^{<}(k)$ in the real-time formalism, we construct the equal-time correlation matrix $C(\bm{k})$ and define the left-handed reduced correlator $C_L(\bm{k}) = P_L C(\bm{k}) P_L$. The corresponding von Neumann entropy, $S_\chi = -\mathrm{Tr}\left[C_L \ln C_L + (1-C_L)\ln(1-C_L)\right]$, characterizes the mixedness of the chirality-reduced subsystem. We show that the reduced correlator retains a nontrivial helicity structure and must therefore be described by its full eigenvalue spectrum rather than by a single scalar occupation probability. The self-consistent dynamical quark mass $M_q(T,\mu_q)$ reproduces the expected QCD-like phase structure, with a second-order transition in the chiral limit and a smooth crossover for finite current quark mass. The chirality-reduced entropy correlates with chiral restoration but is not itself an order parameter; instead, it provides complementary information via the full spectrum of the reduced correlator. Our numerical results show that $S_\chi$ exhibits characteristic nontrivial behavior across the chiral transition region and serves as an information-theoretic diagnostic of reduced chiral-sector mixedness.