Memory Effects and Transport Coefficients for Non-Newtonian Fluids

TL;DR

This paper explores how memory effects influence viscosity and transport coefficients in relativistic non-Newtonian fluids, leading to non-singular hydrodynamic equations and a generalized Green-Kubo-Nakano approach.

Contribution

It introduces a generalized Green-Kubo-Nakano formula for non-Newtonian fluids and analyzes the impact of memory effects on hydrodynamic equations.

Findings

Memory effects lead to non-singular hydrodynamic equations.

A generalized Green-Kubo-Nakano formula for non-Newtonian fluids is derived.

Memory effects influence the calculation of transport coefficients.

Abstract

We discuss the roles of viscosity in relativistic fluid dynamics from the point of view of memory effects. Depending on the type of quantity to which the memory effect is applied, different terms appear in higher order corrections. We show that when the memory effect applies on the extensive quantities, the hydrodynamic equations of motion become non-singular. We further discuss the question of memory effect in the derivation of transport coefficients from a microscopic theory. We generalize the application of the Green-Kubo-Nakano (GKN) to calculate transport coefficients in the framework of projection operator formalism, and derive the general formula when the fluid is non-Newtonian.