Nucleation in systems with multiple stationary states

We consider a reaction diffusion system, far from equilibrium, which has multiple stationary states (phases) for given ranges of external constraints. If two stable phases are put in contact, then in general one phase annihilates the other and in that process there occurs a single front propagation (soliton). We investigate the macroscopic dynamics of the front structure and velocity for two model systems analytically and numerically, and for general reaction-diffusion systems by a suitable perturbation method. The vanishing of the soliton velocity establishes the analogue of the Maxwell construction used in equilibrium thermodynamics. The problem of nucleation of one phase imbedded in another is studied by a stochastic theory. We show that if the reaction dynamics is derived from a generalized potential function then the macroscopic steady states are extrema of the probability distribution. We use this result to obtain an expression for the critical radius of a nucleating phase and confirm the prediction of the stochastic theory by numerical solution of the deterministic macroscopic kinetics for a model system.