Low density form of the free energy for real matter

We prove that the thermodynamic free energy per unit volume of an over‐all neutral system, composed of electrons and nuclei interacting via Coulomb forces, has the low density asymptotic form ${\mathrm{kT\hspace{0.17em}\; \Sigma }}_{\text{α=0}}^s{\rho }^{\alpha }\ln {\rho }^{\alpha }$ . Here ρ^o is the over‐all number density of electrons and ${\rho }^{\alpha }\text{, α=1,···}$ , s the number density of nuclei of species α. This indicates that, as expected on the basis of nonrigorous arguments, any real physical system will become completely ionized as the density approaches zero (at a fixed nonzero temperature).