A stochastic approach to nucleation in finite systems: Theory and computer simulations

A stochastic theory is presented for nucleation and growth of clusters in a finite system. We consider a discrete cluster distribution for which the free energy and the equilibrium probability distribution are derived. The cluster growth and shrinkage occurs by the attachment/evaporation of free particles. The transition probabilities reflect that clusters of different sizes cannot evolve independently due to the limitation of the total particle number and the finite system size.