Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

TL;DR

This paper extends a formula for calculating transport coefficients in relativistic dissipative hydrodynamics to non-Newtonian fluids, ensuring causality and broadening its applicability using the projection operator method.

Contribution

It generalizes the Green-Kubo-Nakano formula for non-Newtonian fluids within relativistic hydrodynamics, maintaining causality and applicability to more diverse situations.

Findings

Derived a new formula for transport coefficients in non-Newtonian fluids.

Extended the GKN formula to relativistic dissipative hydrodynamics.

Ensured the formula reproduces GKN in specific limits.

Abstract

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.