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We investigate the low-temperature thermodynamics of the unitary Fermi gas byintroducing a model based on the zero-temperature spectra of both bosoniccollective modes and fermonic single-particle excitations. We calculate theHelmholtz free energy and from it we obtain the entropy, the internal energyand the chemical potential as a function of the temperature. By using thesequantities and the Landau's expression for the superfluid density we determineanalytically the superfluid fraction, the critical temperature, the first soundvelocity and the second sound velocity. We compare our analytical results withother theoretical predictions and experimental data of ultracold atoms anddilute neutron matter.

Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound