Generalized relativistic second-order spin hydrodynamics from Zubarev's non-equilibrium statistical operator

TL;DR

This paper extends relativistic second-order spin hydrodynamics by incorporating nonlocal correlation effects and expressing transport coefficients via retarded Green's functions, advancing the theoretical framework for spin transport in relativistic fluids.

Contribution

It introduces second-order corrections from nonlocal correlations into spin hydrodynamics and relates transport coefficients to retarded Green's functions, broadening the theoretical understanding.

Findings

Derived additional second-order terms in shear stress, bulk viscous pressure, and charge diffusion currents.

Expressed transport coefficients in terms of retarded Green's functions.

Extended the framework to include spin degrees of freedom with nonlocal correlation effects.

Abstract

Inspired by the work in Ref.[1], which considers the additional second-order contributions arising from nonlocal corrections due to two-point correlation functions of tensors of different ranks at distinct spacetime points, we similarly employ the nonequilibrium statistical operator method to extend this framework to include spin degrees of freedom. In addition to obtaining analogous extra second-order terms in the shear stress tensor, bulk viscous pressure, and charge diffusion currents resulting from such contributions, we further derive additional second-order terms originating from the same mechanism in the charge diffusion currents, rotational stress tensor and the boost heat vector. Furthermore, we express all transport coefficients represented by two-point or three-point correlations in terms of retarded Green's functions.