  We address a possible relation between the expectation value of the Polyakov
loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models
where constituent quarks and the Polyakov loop are coupled in a minimal way. To
this end we use a center symmetry breaking Gaussian model for the Polyakov loop
distribution which accurately reproduces gluodynamics data above the phase
transition in terms of dimension 2 gluon condensate. The role played by the
quantum and local nature of the Polyakov loop is emphasized.
