Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character

TL;DR

This paper analyzes four formulations of perfect spin hydrodynamics, demonstrating their nonlinear causality and stability through nonperturbative methods, and clarifies their thermodynamic consistency across classical and quantum treatments.

Contribution

It provides a comprehensive analysis of multiple formulations of spin hydrodynamics, establishing their causality and stability nonperturbatively and linking thermodynamic currents to generating functions.

Findings

All formulations satisfy divergence-type theory requirements.

Hydrodynamics are shown to be nonlinearly causal and stable.

The approach is nonperturbative, using exact distribution functions.

Abstract

Four formulations of perfect spin hydrodynamics for spin-1/2 particles, distinguished by their treatment of spin (classical vs. quantum) and by the underlying particle statistics (Boltzmann vs. Fermi-Dirac), are analyzed and shown to satisfy the requirements of a divergence-type theory. Moreover, for all the formulations, we define the generating functions associated with the relevant thermodynamic currents and demonstrate that the constructed hydrodynamic theory is nonlinearly causal and stable. The latter is achieved by employing the exact expressions for the distribution functions, indicating a nonperturbative character of our approach.