Generalized relativistic second-order dissipative hydrodynamics: coupling different rank tensors

TL;DR

This work extends the formalism of second-order relativistic dissipative hydrodynamics using Zubarev's non-equilibrium statistical operator (NESO) to identify new nonlocal second-order terms. The key advance is the coupling of two-point correlators between tensors of different ranks, enabled by fluid acceleration, which induces memory effects and nonlocal mixing among shear, bulk, diffusion, and energy flux channels. The authors derive complete second-order evolution equations for the shear stress tensor, bulk viscous pressure, diffusion currents, and energy flux, expressing the new transport coefficients via two- and three-point Green's functions (Kubo-type relations) and showing how three-point correlators enter as nonlinear contributions. This generalized framework clarifies the structure of second-order terms, their memory origins, and provides pathways to compute the coefficients in both strongly and weakly coupled systems, with attention to causality and stability through appropriate rearrangements and memory terms.

Abstract

In this work, we extend the formalism of second-order relativistic dissipative hydrodynamics, developed previously using Zubarev's non-equilibrium statistical operator formalism. By employing a second-order expansion of the statistical operator in terms of hydrodynamic gradients, we demonstrate that new second-order terms emerge due to the coupling of two-point quantum correlators between tensors of differing ranks, evaluated at distinct space-time points. Such terms arise because the presence of the acceleration vector in the system allows Curie's theorem, which governs symmetry constraints, to be extended for constructing invariants from tensors of different ranks evaluated at distinct space-time points. The new terms are identified in the context of a complete set of second-order equations governing the shear-stress tensor, bulk-viscous pressure, and charge-diffusion currents for a generic quantum system characterized by the energy-momentum tensor and multiple conserved charges. Additionally, we identify the transport coefficients associated with these new terms and derive the Kubo formulas expressing the second-order transport coefficients through two- and three-point correlation functions.