title: Kubo formulas for second-order hydrodynamic coefficients.
abstract: At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity η and on five additional "second-order" hydrodynamical coefficients τ(Π), κ, λ₁, λ₂, and λ₃. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient λ₃ can be evaluated directly by Euclidean means and does not in general vanish.
authors.affiliation: Department of Physics, McGill University, 3600 rue University, Montréal, Quebec H3A 2T8, Canada.
authors.forename: Guy D
authors.initials: GD
authors.lastname: Moore
authors.forename: Kiyoumars A
authors.initials: KA
authors.lastname: Sohrabi