Spin polarization of fermions at local equilibrium: Second-order gradient expansion

We present a calculation of the spin polarization of spin-1/2 fermions in a relativistic fluid at local thermodynamic equilibrium at the second order in the gradient expansion, including second-order derivatives. The second-order derivative terms vanish if the local equilibrium hypersurface is the hyperplane 𝑡=const in the collision center-of-mass frame. However, since the freeze-out hypersurface has a nontrivial space-time structure, these terms may result in a nonvanishing contribution to the spin polarization, whose magnitude needs to be assessed with numerical computations.