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Recent consensus on the $N_f=2+1$ equation of state at vanishing chemicalpotential from different lattice-QCD groups has spoiled the previous agreementwith the outcome from the mean-field Polyakov-Nambu-Jona-Lasinio model. In thisletter we review the thermodynamics of the PNJL model introducing two importantaspects needed to describe the pressure computed in the lattice QCD. First, weconsider the thermodynamics of the model beyond the mean-field approach toinclude pseudoscalar and scalar mesonic-like fluctuations into thegrand-canonical potential. This accounts for the hadronic pressure of thesystem below the critical temperature. On the other hand we also implement theback reaction of quarks into the Polyakov-loop effective potential bringing areduction of the pressure above $T_c$ from the Stefan-Boltzmann limit. We get agood agreement with lattice-QCD data at low and moderate temperatures, openingthe door to a straightforward extension to finite chemical potential.

Equation of state of a quark-Polyakov loop-meson mixture in the PNJL model at finite temperature