Pedro Balodis Matesanz, Jan Philip Solovej On the asymptotic exactness of Thomas-Fermi theory in the thermodynamic limit. (71K, LATeX 2e) ABSTRACT. In this paper we obtain a new version of stability of matter, which in particular shows that Thomas-Fermi theory is asymptotically correct in the limit of large nuclear charges uniformly in the number of nuclei. As a consequence we give a new lower bound on the volume of matter with an improved dependence on the nuclear charges.