Two-loop hard-thermal-loop thermodynamics with quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N