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

Generalized Beth-Uhlenbeck approach to the equation of state for quark-hadron matter