Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically-trapped Fermi gas in the unitary limit. Our calculations rest on a study of the equation of state of a uniform gas using three distinct perturbation schemes, compared to Monte-Carlo results. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly-interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.