  We present a study of the thermodynamics of the massless free Dirac field at
equilibrium with axial charge, angular momentum and and external
electromagnetic field to assess the interplay between chirality, vorticity and
electromagnetic field in relativistic fluids. After discussing the general
features of global thermodynamic equilibrium in quantum relativistic
statistical mechanics, we calculate the thermal expectation values. Axial
imbalance and electromagnetic field are included non-perturbatively by using
the exact solutions of the Dirac equation, while a perturbative expansion is
carried out in thermal vorticity. It is shown that the chiral vortical effect
and the axial vortical effect are not affected by a constant homogeneous
electromagnetic field.
