On the Coefficients of a Hyperbolic Hydrodynamic Model

TL;DR

This paper derives a hyperbolic hydrodynamic equation from a nonequilibrium density operator and provides microscopic formulas for its coefficients, linking them to correlation lengths in statistical mechanics.

Contribution

It introduces a new derivation of hyperbolic hydrodynamics with explicit microscopic formulas for all coefficients, connecting macroscopic equations to statistical mechanics.

Findings

Derived a hyperbolic hydrodynamical equation from the Nakajima-Zubarev formalism.

Obtained microscopic Kubo-formulas for all coefficients in the model.

Expressed Israel-Stewart coefficients as current-weighted correlation lengths.

Abstract

Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive a hyperbolic hydrodynamical equation. Microscopic Kubo-formulas for all coefficients in the hyperbolic hydrodynamics are obtained. Coefficients $\alpha_{i}$'s and $\beta_{i}$'s in the Israel-Stewart equation are given as current-weighted correlation lengths which are to be calculated in statistical mechanics.