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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 (PNJL) 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 endpoint (CEP). On the boundary of the first-order transition, $ζ/s$ shows a non-monotonic 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.