Communication: On nucleation statistics in small systems

Non-stationary random formation of stable nuclei from a small metastable system is considered. Distribution of waiting times to observe the first nucleus is examined, and it is shown that the steady-state nucleation rate is given by inverse of the standard deviation, which is independent of the post-critical size n where the nucleus is detected. The mean time, on the other hand, is n-sensitive and contains additional information on transient nucleation and growth effects. The method is applied to Monte Carlo data on nucleation in a cold two-dimensional Ising ferromagnet with Metropolis dynamics, where nucleation rates obtained earlier from low-temperature cluster expansions can provide a strict independent test.