  We derive the Polyakov-loop thermodynamic potential in the perturbative
approach to pure SU(3) Yang-Mills theory. The potential expressed in terms of
the Polyakov loop in the fundamental representation corresponds to that of the
strong-coupling expansion, of which the relevant coefficients of the gluon
energy distribution are specified by characters of the SU(3) group. At high
temperature, the potential exhibits the correct asymptotic behavior, whereas at
low temperature, it disfavors gluons as appropriate dynamical degrees of
freedom. To quantify the Yang-Mills thermodynamics in confined phase, we
introduce a hybrid approach which matches the effective gluon potential to that
of glueballs, constrained by the QCD trace anomaly in terms of dilaton fields.
