Fate of spin polarization in a relativistic fluid: An entropy-current analysis

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.