  We calculate the constitutive equations of the stress-energy tensor and the
currents of the free massless Dirac field at thermodynamic equilibrium with
acceleration and rotation and a conserved axial charge by using the density
operator approach. We carry out an expansion in thermal vorticity to the second
order with finite axial chemical potential $\mu_A$. The obtained coefficients
of the expansion are expressed as correlators of angular momenta and boost
operators with the currents. We confirm previous observations that the axial
chemical potential induces non-vanishing components of the stress-energy tensor
at first order in thermal vorticity due to breaking of parity invariance of the
density operator with $\mu_A \ne 0$. The appearance of these components might
play an important role in chiral hydrodynamics.
