  A selfconsistent thermodynamic $T$-matrix approach is deployed to study the
microscopic properties of the quark-gluon plasma (QGP), encompassing both
light- and heavy-parton degrees of freedom in a unified framework. The starting
point is a relativistic effective Hamiltonian with a universal color force. The
input in-medium potential is quantitatively constrained by computing the
heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to
pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied
to compute the equation of state (EoS) of the QGP in a two-particle irreducible
formalism including the full off-shell properties of the selfconsistent
single-parton spectral functions and their two-body interaction. In particular,
the skeleton diagram functional is fully resummed to account for emerging bound
and scattering states as the critical temperature is approached from above. We
find that the solution satisfying three sets of lQCD data (EoS, HQ free energy
and quarkonium correlator ratios) is not unique. As limiting cases we discuss a
weakly-coupled solution (WCS) which features color-potentials close to the free
energy, relatively sharp quasiparticle spectral functions and weak hadronic
resonances near $T_{\rm c}$, and a strongly-coupled solution (SCS) with a
strong color potential (much larger than the free energy) resulting in broad
non-quasiparticle parton spectral functions and strong hadronic resonance
states which dominate the EoS when approaching $T_{\rm c}$.
