Kubo Formulae for Second-Order Hydrodynamic Coefficients

TL;DR

This paper derives Kubo relations for second-order hydrodynamic coefficients in conformal relativistic hydrodynamics, linking them to equilibrium correlation functions, and provides a method to evaluate lambda3 directly.

Contribution

It introduces explicit Kubo formulas for five second-order hydrodynamic coefficients, including a novel Euclidean evaluation method for lambda3.

Findings

Kubo relations for all five second-order coefficients derived

Lambda3 can be computed via Euclidean methods and generally does not vanish

Provides a practical approach for calculating second-order hydrodynamic parameters

Abstract

At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity eta and on five additional "second-order" hydrodynamical coefficients tauPi, kappa, lambda1, lambda2, and lambda3. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded 3-point correlation functions of the stress tensor. We show that the coefficient lambda3 can be evaluated directly by Euclidean means and does not in general vanish.