  We outline an approach to a unified equation of state for quark-hadron matter
on the basis of a $\Phi-$derivable approach to the generalized Beth-Uhlenbeck
equation of state for a cluster decomposition of thermodynamic quantities like
the density. To this end we summarize the cluster virial expansion for nuclear
matter and demonstrate the equivalence of the Green's function approach and the
$\Phi-$derivable formulation. For an example, the formation and dissociation of
deuterons in nuclear matter is discussed. We formulate the cluster
$\Phi-$derivable approach to quark-hadron matter which allows to take into
account the specifics of chiral symmetry restoration and deconfinement in
triggering the Mott-dissociation of hadrons. This approach unifies the
description of a strongly coupled quark-gluon plasma with that of a
medium-modified hadron resonance gas description which are contained as
limiting cases. The developed formalism shall replace the common two-phase
approach to the description of the deconfinement and chiral phase transition
that requires a phase transition construction between separately developed
equations of state for hadronic and quark matter phases. Applications to the
phenomenology of heavy-ion collisions and astrophysics are outlined.
