  The trace anomaly of gluodynamics encodes the breakdown of classical scale
invariance due to interactions around the deconfinement phase transition. While
it is expected that at high temperatures perturbation theory becomes applicable
we show that current lattice calculations are far from the perturbative regime
and are dominated instead by inverse even power corrections in the temperature,
while the total perturbative contribution is estimated to be extremely small
and compatible with zero within error bars. We provide an interpretation in
terms of dimension-two gluon condensate of the dimensionally reduced theory
which value agrees with a similar analysis of power corrections from available
lattice data for the renormalized Polyakov loop and the heavy quark-antiquark
free energy in the deconfined phase of QCD.
