  We study the QCD equation of state and other thermodynamic observables
including the isentropic trajectories and the speed of sound. These observables
are of eminent importance for the understanding of experimental results in
heavy ion collisions and also provide a QCD input for studies of the timeline
of heavy-ion-collisions with hydrodynamical simulations. They can be derived
from the quark propagator whose gap equation is solved within a minimal
approximation to the Dyson-Schwinger equations of QCD at finite temperature and
density. This minimal approximation aims at a combination of computational
efficiency and simplification of the truncation scheme while maintaining
quantitative precision. This minimal DSE scheme is confronted and benchmarked
with results for correlation functions and observables from first principles
QCD lattice at vanishing density and quantitative functional approaches at
finite density.
