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

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.