Ideal spin hydrodynamics from Wigner function approach

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization $\chi_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and $\chi_s$.