We present numerical results on the static quark--anti-quark grand canonical potential in full QCD at non-vanishing temperature ($T$) and quark chemical potential ($mu$). Non-zero $mu$-s are reached by means of multi-parameter reweighting. The dynami
cal staggered simulations were carried out for $n_f=2+1$ flavors with physical quark masses on $4times 12^3$ lattices.
We present results of a hybrid Monte-Carlo algorithm for dynamical, $n_f=2$, four-dimensional QCD with overlap fermions. The fermionic force requires careful treatment, when changing topological sectors. The pion mass dependence of the topological su
sceptibility is studied on $6^4$ and $12cdot 6^3$ lattices. The results are transformed into physical units.
We compare our 2+1 flavor, staggered QCD lattice results with a quasiparticle picture. We determine the pressure, the energy density, the baryon density, the speed of sound and the thermal masses as a function of T and $mu_B$. For the available therm
odynamic quantities the difference is a few percent between the results of the two approaches. We also give the phase diagram on the $mu_B$--T plane and estimate the critical chemical potential at vanishing temperature.