Bulk viscosity from hydrodynamic fluctuations with relativistic hydro-kinetic theory

Hydro-kinetic theory of thermal fluctuations is applied to a non-conformal relativistic fluid. Solving the hydro-kinetic 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 non-equilibrium 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 non-conformal nature of the equation of state and is modestly enhanced near the QCD deconfinement temperature.