Second-order spin hydrodynamics from Zubarev's nonequilibrium statistical operator formalism

TL;DR

This paper derives second-order relativistic spin hydrodynamics equations using Zubarev's formalism, incorporating spin density as an independent variable and revealing new transport coefficients and thermodynamic forces related to spin effects.

Contribution

It introduces a second-order formulation of spin hydrodynamics including spin density as an independent variable, and derives new transport coefficients and evolution equations using Zubarev's formalism.

Findings

Derived second-order dissipative tensors in spin hydrodynamics.

Identified new thermodynamic forces related to spin chemical potential.

Established evolution equations for spin-related tensors.

Abstract

Using the Zubarev's nonequilibrium statistical operator formalism, we derive the second-order expression for the dissipative tensors in relativistic spin hydrodynamics, {\em viz.} rotational stress tensor ($\tau_{\mu\nu}$), boost heat vector ($q_\mu$), shear stress tensor ($\pi_{\mu\nu}$), and bulk viscous pressure ($\Pi$). The first two ($\tau_{\mu\nu}$ and $q_\mu$) emerge due to the inclusion of the antisymmetric part in the energy-momentum tensor, which, in turn, governs the conservation of spin angular momentum ($\Sigma^{\alpha\mu\nu}$). As a result, new thermodynamic forces, generated due to the antisymmetric part of $T_{\mu \nu}$, contain the spin chemical potential. In this work, we have also taken the spin density ($S^{\mu \nu}$) as an independent thermodynamic variable, in addition to the energy density and particle density, thereby resulting in two novel transport coefficients given by the correlation between spin density tensor and rotational stress tensor and vice versa. Additionally, the newly found terms in $\pi_{\mu\nu}$ and $\Pi$ are the artifacts of the new thermodynamic forces that arise due to the antisymmetric part of $T^{\mu \nu}$. Finally, we have derived the evolution equations for the aforesaid tensors: $\tau_{\mu\nu}$, $q_\mu$, $\pi_{\mu\nu}$, and $\Pi$.