Summary: In this paper we study the ground state energy of a classical gas. Our interest centers mainly on Coulomb systems. We obtain some new lower bounds for the energy of a Coulomb gas. As a corollary of our results we can show that a fermionic system with relativistic kinetic energy and Coulomb interaction is stable. More precisely, let \(H_N(\alpha)\) be the \(N\)-particle Hamiltonian \[ H_N(\alpha)=\alpha\sum^N_{i=1}(-\Delta_i)^{1/2}+\sum_{i<j} |x_i-x_j|^{-1}-\sum_{i,j}|x_i-R_j|^{-1}+\sum_{i<j}|R_i-R_j |^{-1}, \] where \(\Delta_i\) is the Laplacian in the variable \(x_i\in{\mathbb{R}}^3\) and \(R_1,\cdots,R_N\) are fixed points in \({\mathbb{R}}^3\). We show that for sufficiently large \(\alpha\), independent of \(N\), the Hamiltonian \(H_N(\alpha)\) is nonnegative on the space of square integrable functions \(\psi(x_1,\cdots,x_N)\) which are antisymmetric in the variables \(x_i, 1\leq i\leq N\).