Ideal Spin Hydrodynamics from the Wigner Function Approach

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