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We present a unified approach to the thermodynamics of hadron-quark-gluonmatter at finite temperatures on the basis of a quark cluster expansion in theform of a generalized Beth-Uhlenbeck approach with a generic ansatz for thehadronic phase shifts that fulfills the Levinson theorem. The change in thecomposition of the system from a hadron resonance gas to a quark-gluon plasmatakes place in the narrow temperature interval of $150 - 185$ MeV where theMott dissociation of hadrons is triggered by the dropping quark mass as aresult of the restoration of chiral symmetry. The deconfinement of quark andgluon degrees of freedom is regulated by the Polyakov loop variable thatsignals the breaking of the $Z(3)$ center symmetry of the color $SU(3)$ groupof QCD. We suggest a Polyakov-loop quark-gluon plasma model with$\mathcal{O}(\alpha_s)$ virial correction and solve the stationarity conditionof the thermodynamic potential (gap equation) for the Polyakov loop. Theresulting pressure is in excellent agreement with lattice QCD simulations up tohigh temperatures.

Quark cluster expansion model for interpreting finite-T lattice QCD thermodynamics