  The hydrodynamic coefficients in the axial current are calculated on the
basis of the equilibrium quantum statistical density operator in the third
order of perturbation theory in thermal vorticity tensor both for the case of
massive and massless fermions. The coefficients obtained describe third-order
corrections to the Chiral Vortical Effect and include the contribution from
local acceleration. We show that the methods of the Wigner function and the
statistical density operator lead to the same result for an axial current in
describing effects associated only with vorticity when the local acceleration
is zero, but differ in describing mixed effects for which both acceleration and
vorticity are significant simultaneously.
