Bulk viscosity from hydrodynamic fluctuations with relativistic hydrokinetic theory

Hydrokinetic theory of thermal fluctuations is applied to a nonconformal relativistic fluid. Solving the hydrokinetic equations for an isotropically expanding background we find that hydrodynamic fluctuations give ultraviolet divergent contributions to the energy-momentum tensor. After shifting the temperature to account for the energy of nonequilibrium modes, the remaining divergences are renormalized into local parameters, e.g., pressure and bulk viscosity. We also confirm that the renormalization of the pressure and bulk viscosity is universal by computing them for a Bjorken expansion. The fluctuation-induced bulk viscosity reflects the nonconformal nature of the equation of state and is modestly enhanced near the QCD deconfinement temperature.

Figure 1

A fluctuation-induced bulk viscosity bound as a function of temperature, Eq. (1), for lattice parametrization of the QCD equation of state and shear viscosity over entropy $\eta /s=1/\left(4\pi \right)$ [26]. The UV bound of hydrodynamic fluctuations $\mathrm{\Lambda }$ is varied between $2T$ and $4T$.