  We show that the stress-energy tensor has additional terms with respect to
the ideal form in states of global thermodynamic equilibrium in flat spacetime
with non-vanishing acceleration and vorticity. These corrections are of quantum
origin and their leading terms are second order in the gradients of the
thermodynamic fields. Their relevant coefficients can be expressed in terms of
correlators of the stress-energy tensor operator and the generators of the
Lorentz group. With respect to previous assessments, we find that there are
more second order coefficients and that all thermodynamic functions including
energy density receive acceleration and vorticity dependent corrections.
Notably, also the relation between \rho and p, that is the equation of state,
is affected by acceleration and vorticity. We have calculated the corrections
for a free real scalar field -- both massive and massless -- and we have found
that they increase, particularly for a massive field, at very high acceleration
and vorticity and very low temperature. Finally, these non-ideal terms depend
on the explicit form of the stress-energy operator, implying that different
stress-energy tensor of the scalar field -- canonical or improved -- are
thermodynamically inequivalent.
