# Relativistic fluid dynamics of spin-polarized systems of particles

## TL;DR

This paper reviews the development of relativistic perfect-fluid hydrodynamics for spin-1/2 particles, presents numerical solutions, and highlights the impact of initial spin polarization on particle polarization at freeze-out.

## Contribution

It introduces and analyzes hydrodynamic equations incorporating spin polarization, with numerical solutions demonstrating the significance of initial spin conditions.

## Key findings

- Initial spin polarization influences particle polarization at freeze-out.
- Numerical solutions show the evolution of spin polarization in relativistic fluids.
- The framework advances understanding of spin dynamics in high-energy systems.

## Abstract

We review basic ingredients of the recently introduced perfect-fluid hydrodynamic equations for particles with spin one-half. For a quasi-realistic setup, first numerical solutions for various hydrodynamic variables including the spin polarization tensor are presented. Our results indicate that the initial spin polarization of the hottest region may play a dominant role in the polarization of particles at freeze-out.