Bulk viscosity of quark matter across the QCD phase transitions

Based on the kinetic theory with relaxation time approximation, we investigate the bulk viscosity ( ζ ) and its ratio to shear viscosity ( ζ / η ) of quark matter at finite temperature and chemical potential with the in-medium particle masses derived in the 2 + 1 flavor Polyakov-loop improved Nambu–Jona-Lasinio model. We explore the behaviors of specific bulk viscosity ( ζ / s ) and ζ / η across different QCD phase transitions, including the Mott phase transition, the chiral crossover, and the first-order transition with the associated metastable phase. The calculation shows that both ζ / s and ζ / η are extremely small at high temperatures, approaching the nature of a conformal theory. Larger ζ / s and ζ / η are derived near the chiral phase transition at finite temperature. Along the chiral crossover line, ζ / s and ζ / η generally increase with decreasing temperature, though ζ / η exhibits a slight decline near the critical end point. On the boundary of the first-order transition, ζ / s shows a nonmonotonic variation with temperature. Furthermore, an additional peak structure emerges beyond the chiral phase boundary for both ζ / s and ζ / η , with magnitudes even exceeding those near the chiral crossover of u , d quarks. Our analysis indicates this peak originates from the chiral crossover transformation of strange quark.