Spin density from second order transport in fluids

We study the hydrodynamics of a charged fluid with spin degrees of freedom. We argue that, in a conformal field theory in 3+1 dimensions, the spin density is related to a linear combination of standard second-order transport coefficients, and an additional term quadratic in the gauge- and mixed gauge-gravitational anomaly coefficients. We compute the spin density in several free and holographic theories and compare the results.