We calculate the equation of state at non-zero temperature and density from first principles in two-, three- and four-color QCD with two fermion flavors in the fundamental and two-index, antisymmetric representation. By matching low-energy results (from a `hadron resonance gas') to high-energy results from (resummed) perturbative QCD, we obtain results for the pressure and trace anomaly that are in quantitative agreement with full lattice-QCD studies for three colors at zero chemical potential. Our results for non-zero chemical potential at zero temperature constitute predictions for the equation of state in QCD-like theories that can be tested by traditional lattice studies for two-color QCD with two fundamental fermions and four-color QCD with two two-index, antisymmetric fermions. We find that the speed of sound squared at zero temperature can exceed one third, which may be relevant for the phenomenology of high-mass neutron stars.

16 pages, 8 figures