  Exact relations between the QCD thermal pressure and the trace anomaly are
derived. These are used, first, to prove the equivalence of the thermodynamic
and the hydrodynamic pressure in equilibrium in the presence of the trace
anomaly, closing a gap in previous arguments. Second, in the temporal axial
gauge a formula is derived which expresses the thermal pressure in terms of a
Dyson-resummed two-point function. This overcomes the infrared problems
encountered in the conventional perturbation-theory approach.
