Bulk viscosity from hydrodynamic fluctuations with relativistic hydro-kinetic theory

TL;DR

This paper applies hydro-kinetic theory to a relativistic fluid, revealing how thermal fluctuations influence bulk viscosity and require renormalization, with implications for QCD near the deconfinement temperature.

Contribution

It introduces a hydro-kinetic approach to compute fluctuation-induced bulk viscosity in non-conformal relativistic fluids, including renormalization procedures.

Findings

Hydrodynamic fluctuations cause ultraviolet divergences in the energy-momentum tensor.

Renormalization of pressure and bulk viscosity is universal across expansion types.

Bulk viscosity is modestly increased near the QCD deconfinement temperature.

Abstract

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.