Kubo formulas for thermodynamic transport coefficients

TL;DR

This paper derives Kubo formulas for all thermodynamic transport coefficients in relativistic fluids, linking them to equilibrium correlation functions, and computes these coefficients in free field theories.

Contribution

It provides the first comprehensive derivation of Kubo formulas for all second-order thermodynamic coefficients in relativistic fluids with and without a U(1) current.

Findings

All parity-preserving coefficients expressed via two-point functions.

Parity-violating coefficients require three-point functions.

Computed coefficients in several free field theory examples.

Abstract

Uncharged relativistic fluids in 3+1 dimensions have three independent thermodynamic transport coefficients at second order in the derivative expansion. Fluids with a single global $U(1)$ current have nine, out of which seven are parity preserving. We derive the Kubo formulas for all nine thermodynamic transport coefficients in terms of equilibrium correlation functions of the energy-momentum tensor and the current. All parity-preserving coefficients can be expressed in terms of two-point functions in flat space without external sources, while the parity-violating coefficients require three-point functions. We use the Kubo formulas to compute the thermodynamic coefficients in several examples of free field theories.