We study a system of N interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as 1/N and with an effective semi-classical parameter h = N^{-1/d} where d is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature. In the derivation of the latter arises the fermionic entropy s(x) = x log x + (1-x) log(1-x). We also treat the dilute case, when the two body interaction potential is scaled like N^{d \eta} w(N^{\eta} x).

(Joint work with M. Lewin and P. Madsen)

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