Stochastic fluctuations and the relaxation time in transient relativistic fluids

TL;DR

This paper investigates the ratio of shear viscosity to relaxation time in relativistic fluids, proposing a thermodynamic definition, deriving it from kinetic theory and holography, and analyzing the impact of fluctuations on stability.

Contribution

It introduces a thermodynamic definition of the shear viscosity to relaxation time ratio and derives it for kinetic and holographic theories, also studying fluctuation effects.

Findings

The ratio is a thermodynamic quantity from the shear-stress correlator.

The ratio is interaction-independent in kinetic theory.

Fluctuations do not compromise causality or stability in the model.

Abstract

We argue that the ratio between the shear viscosity and the shear relaxation time, $\eta/\tau_\pi$, should be defined as a thermodynamic quantity obtained from the equal-time symmetric correlator of the shear-stress tensor. In kinetic theory, we show that this ratio does not depend on the type of interaction. Similarly, an exact expression for this ratio is obtained for holographic gauge theories. We also determine how stochastic fluctuations change $\eta/\tau_\pi$ in transient relativistic hydrodynamics and show that thermal fluctuations do not spoil causality and stability.