Equilibrium and metastable states of classical systems

We formulate a characterization of equilibrium and metastable states of classical hard-core continuous systems in terms of certain global and local stability conditions. The equilibrium states are assumed to be those that are both locally and globally stable; the metastable states are assumed to be those that are locally, but not globally, stable, and that possess also a certain restricted global stability. It is found that a certain specified class of systems with appropriately weakly tempered, or long range forces, can support metastable states, possessing bona fide thermodynamic properties, whose pressure functions are real analytic continuations in the chemical potential of those of some equilibrium phases. This result is complementary to that of Lanford and Ruelle, concerning the absence of metastable states of systems with strongly tempered forces.