Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity

Abstract We develop a relativistic (quasi-)hydrodynamic framework, dubbed gyrohydrodynamics, to describe the fluid dynamics of many-body systems with spin under strong vorticity based on entropy-current analysis. This framework generalizes the recently developed spin hydrodynamics to the regime where the spin density is at the leading order in derivatives but suppressed by another small parameter, the Planck constant ℏ, due to its quantum nature. Our analysis shows that the complete first-order constitutive relations of gyrohydrodynamics involve 17 transport coefficients and are highly anisotropic.