  A unified equation of state for quark-hadron matter is presented in the
generalized Beth-Uhlenbeck form. It follows from a $\Phi-$derivable approach to
the thermodynamic potential where the ansatz for the $\Phi$ functional contains
all 2PI diagrams at two-loop order formed with quark cluster Green's functions
for quark, diquark, meson and baryon propagators. We present numerical results
using an effective model for the generic behaviour of hadron masses and phase
shifts at finite temperature which shares basic features with recent
developments within the PNJL model for correlations in quark matter. We obtain
the transition between a hadron resonance gas phase and the quark gluon plasma
where the Mott dissociation of hadrons is encoded in the hadronic phase shifts.
The resulting thermodynamics is in very good agreement with recent lattice QCD
simulations.
