# Fate of spin polarization in a relativistic fluid: An entropy-current analysis

## TL;DR

This paper develops relativistic hydrodynamic equations incorporating spin dynamics, revealing that spin density dissipates over time due to mutual conversion with orbital angular momentum, constrained by thermodynamic principles.

## Contribution

It introduces a novel entropy-current based derivation of relativistic hydrodynamics with spin, including constitutive relations and spin-diffusion modes.

## Key findings

- Spin density is damped out after a characteristic time.
- Spin and orbital angular momentum are mutually convertible.
- Hydrodynamic equations are constrained by thermodynamics.

## Abstract

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.