  Using a unified hadron-quark effective model for the QCD equation of state,
this paper studies the phase structure of strongly interacting matter in a wide
range of temperature and baryonchemical potential. At small potentials the
model yields a smooth cross-over to chirally restored matter with a transition
temperature and curvature in line with recent lattice QCD estimates and thermal
model fits of freeze-out curves. Trajectories of constant entropy per net
baryon number show a clear dependence on the particle composition in the model
and on repulsive vector field interactions. Although the model might feature a
critical end-point at a rather high baryonchemical potential and low
temperature, probing it in heavy-ion collisions might be highly challenging due
to a large thermodynamic spread of matter in the collision fireball.
