Comparative study of the finite-temperature thermodynamics of a unitary Fermi gas

The finite-temperature thermodynamics of a unitary Fermi gas is studied in detail. The chemical potential, energy density, and entropy are given analytically with the quasilinear approximation. The ground-state energy agrees with previous theoretical and experimental results. Recently, the generalized exclusion statistics is applied to the discussion of the finite-temperature unitary Fermi-gas thermodynamics. A concrete comparison between the two different approaches is performed. Emphasis is made on the behavior of the entropy per particle. In physics, the slope of entropy gives the information on the effective fermion mass m(*)/m in the low-temperature strongly degenerate region. Compared with m(*)/m approximate to 0.70 < 1 given in terms of the generalized exclusion statistics, our quasilinear approximation determines that m(*)/m approximate to 1.11>1.