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Abstract

Abstract: We study chiral symmetry restoration in hot and dense quark matter using the von Neumann chirality entropy within the in-medium Nambu--Jona-Lasinio (NJL) model. Starting from the lesser Green’s function $G^{<}(k)$, we construct the chirality-reduced correlator $C_L = P_L G^{<} P_L$ and define the associated entropy $S_\chi = -\mathrm{Tr}\left[C_L \ln C_L + (1 - C_L)\ln(1 - C_L)\right]$ to quantify quantum entanglement between left- and right-handed quark sectors. The dynamical quark mass $M_q(T,\mu_q)$ reproduces the expected QCD-like phase structure, showing a second-order transition in the chiral limit and a smooth crossover for finite current quark mass. The chirality entropy $S_\chi$ increases monotonically with temperature and chemical potential and approaches a maximal value as $M_q \to 0$. Analyzing its critical behavior, we find a scaling exponent $\beta_{S_\chi} \simeq 1$, distinct from that of the chiral order parameter. This indicates that $S_\chi$ is not an order parameter but a thermodynamic measure of chiral quantum decoherence. Our results demonstrate that chiral symmetry restoration and chiral decoherence are not identical phenomena, and that the chirality entropy reveals information inaccessible to conventional symmetry-breaking observables.