Relativistic fluid dynamics with spin
Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the spin tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extend the standard picture of perfect fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space time analyzes of the evolution of spin and polarization in various physical systems including high energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity spin alignment, corresponds to a special solution of the spin hydrodynamical equations.