A rigorous study of metastability in a continuous model

We consider the classical continuous Widom and Rowlinson model. We follow the general method for describing metastable states proposed by Penrose and Lebowitz. Suitably restricting the set of the allowed configurations, we construct a nonequilibrium state describing a pure phase. Starting from the natural time evolution of the system, we rigorously prove that when both the activities are sufficiently large and close enough together, the relaxation time per unit volume can be made very large.