  Based on a thermodynamic $T$-matrix approach we extract the potential $V$
between two static charges in the quark-gluon plasma (QGP) from fits to the
pertinent lattice-QCD free energy. With suitable relativistic corrections we
utilize this new potential to compute heavy-quark transport coefficients and
compare the results to previous calculations using either $F$ or $U$ as
potential. We then discuss a generalization of the $T$-matrix re-summation to a
"matrix $\log$" re-summation of $t$-channel diagrams for the grand partition
function of the QGP in the Luttinger-Ward skeleton diagram formalism. With $V$
as a non-perturbative driving kernel in the light-parton sector, we obtain the
QGP equation of state from fits to lattice-QCD data. The resulting light-parton
spectral functions are characterized by large thermal widths at small momenta,
indicating the dissolution of quasi-particles in a strongly coupled QGP.
