Microscopic Origin of the Shear Relaxation Time in Causal Dissipative Fluid Dynamics

TL;DR

This paper derives the shear relaxation time in causal dissipative fluid dynamics from microscopic theory, showing it is determined by the pole of the retarded Green's function nearest to the origin, thus linking microscopic properties to macroscopic fluid behavior.

Contribution

It establishes a direct method to compute shear relaxation time from microscopic theory, clarifying its microscopic origin in Israel-Stewart-type models.

Findings

Shear relaxation time equals the inverse of the Green's function pole nearest to the origin.

The relaxation time is a microscopic time scale, not a fluid-dynamical one.

Provides a theoretical framework connecting microscopic theory with macroscopic fluid dynamics.

Abstract

In this paper we show how to compute the shear relaxation time from an underlying microscopic theory. We prove that the shear relaxation time in Israel-Stewart-type theories is given by the inverse of the pole of the corresponding retarded Green's function, which is nearest to the origin in the complex energy plane. Consequently, the relaxation time in such theories is a microscopic, and not a macroscopic, i.e., fluid-dynamical time scale.