Non-Equilibrium Trace Anomaly And Bulk Viscosity in Heavy Ion Collisions From Kinetic Theory

Abstract

We investigate the far-from-equilibrium dynamics and transport properties of a relativistic massive gas obeying Maxwell-Boltzmann (MB), Bose-Einstein (BE), and Fermi-Dirac (FD) statistics undergoing a boost-invariant Bjorken expansion. We solve the relativistic Boltzmann equation in the relaxation-time approximation (RTA) using the method of moments. We focus on the time evolution of the trace of the energy-momentum tensor ${\Theta }^{\mu }{}_{\mu }$ and the bulk viscous pressure $\Pi$, which are key diagnostics of conformal-symmetry breaking in the rapidly evolving fireball created in heavy-ion collisions. We find that the non-equilibrium quantity ${\Theta }^{\mu }{}_{\mu }/T^4$ exhibits a non-monotonic time dependence, with a local maximum at early times and a pronounced dip around the characteristic relaxation time scale ${\tau }_R$. We further show that the scaled bulk pressure $\Pi /P_0$, where $P_0$ denotes the isotropic equilibrium pressure, depends sensitively on the particle statistics. In addition, increasing the initial chemical potential enhances the magnitudes of both $\Pi$ and ${\Theta }^{\mu }{}_{\mu }/T^4$. Finally, by initializing the system with random non-equilibrium configurations, we demonstrate that the evolution of the scaled bulk pressure and the pressure anisotropy converges to a common late-time solution.