  We consider a quantum system of non-interacting fermions at temperature T, in
the framework of linear response theory. We show that semiclassical theory is
an appropriate framework to describe some of their thermodynamic properties, in
particular through asymptotic expansions in $\hbar$ (Planck constant) of the
dynamical susceptibilities. We show how the closed orbits of the classical
motion in phase space manifest themselves in these expansions, in the regime
where T is of the order of $\hbar$.
