Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator

TL;DR

This paper derives relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's formalism, identifying new transport coefficients and relaxation equations expressed via equilibrium correlations.

Contribution

It provides a systematic derivation of second-order hydrodynamics from a quantum statistical perspective, introducing new transport coefficients and Kubo formulas.

Findings

Derived relaxation equations for shear-stress, bulk-viscous pressure, and charge currents.

Identified new second-order transport coefficients in terms of equilibrium correlations.

Established Kubo-type formulas for these second-order coefficients.

Abstract

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy-momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients.