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

Four formulations of perfect spin hydrodynamics for spin- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:math> 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.