A stochastic theory of cluster growth in homogeneous nucleation

A critical cluster in homogeneous nucleation can be defined in two ways. Thermodynamically, the size of the critical cluster corresponds to a maximum of the free energy of the system; kinetically the critical cluster is defined such that all supercritical clusters grow and all others decay. We describe the evolution of a cluster by a postulated stochastic master equation in which the transition probabilities are given by a formula proposed by Langer. We derive from these assumptions, by a path integral method, an equation for the most probable evolution of the size of the cluster and show thereby that under these circumstances the two definitions are equivalent.