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

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 systematic expansion the energy–momentum tensor and charge current to second order in deviations from equilibrium. As concrete example, we obtain relaxation equations shear-stress tensor, bulk-viscous pressure, charge-diffusion currents required close set motion hydrodynamics. also identify transport coefficients which describe processes express them terms equilibrium correlation functions, thus establishing Kubo-type formulas coefficients.