Spinodal expansions in the study of the decay of deeply quenched metastable states

We study the decay of close to the spinodal metastable states through isobaric processes. One usually studies these processes by considering a Landau expansion of the free energy around the critical point, which may lie far away from the region of phase space where the dynamics are relevant, both in temperature and pressure. By relying on the critical nature of the spinodal points, apparent from the divergence of the compressibility and the presence of scaling in their vicinity, we propose an alternate view. By using, as a toy model, an analytical equation of state which describes a system that can exist in a liquid or vapor phase, we construct a generalized Gibbs-Landau free energy expansion around any spinodal point, which includes the critical point as a special case. This expansion is then used to study the dynamics of nucleation of the stable phase out of the metastable region.