Ideal relativistic fluid limit for a medium with polarization

We use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid of which the constituent degrees of freedom have microscopic polarization. We discuss the meaning of such a system and argue that it is the first term in the Effective Field Theory (EFT) appropriate for describing polarization observables in heavy ion collisions, such as final-state particle polarization and chiral magnetic and vortaic effects. We show that this system will generally require nondissipative dynamics at higher order in the gradient than second order, leading to potential stability issues known with such systems. We comment on the significance of this in the light of conjectured lower limits on viscosity.