Thermodynamic stability in relativistic viscous and spin hydrodynamics

TL;DR

This paper uses thermodynamic stability analysis to establish conditions ensuring causality and stability in relativistic viscous and spin hydrodynamics, providing more stringent constraints when viscous tensors are present.

Contribution

It derives thermodynamic stability conditions for second-order relativistic hydrodynamics and spin hydrodynamics, linking them to causality and linear mode analysis results.

Findings

Thermodynamic stability conditions match linear mode analysis for non-viscous cases.

More stringent stability constraints are found with viscous tensors.

Conditions can guarantee causality and stability in hydrodynamic models.

Abstract

We have applied thermodynamic stability analysis to derive the stability and causality conditions for conventional relativistic viscous hydrodynamics and spin hydrodynamics. We obtain the thermodynamic stability conditions for second-order relativistic hydrodynamics with shear and bulk viscous tensors, finding them identical to those derived from linear mode analysis. We then derive the thermodynamic stability conditions for minimal causal extended second-order spin hydrodynamics in canonical form, both with and without viscous tensors. Without viscous tensors, the constraints from thermodynamic stability exactly match those from linear mode analysis. In the presence of viscous tensors, the thermodynamic stability imposes more stringent constraints than those obtained from linear mode analysis. Our results suggest that conditions derived from thermodynamic stability analysis can guarantee both causality and stability in linear mode analysis.