Non-Markovian dynamics of clusters during nucleation

Most theories of homogeneous nucleation are based on a Fokker-Planck-like description of the behavior of the mass of clusters. Here we will show that these approaches are incomplete for a large class of nucleating systems, as they assume the effective dynamics of the clusters to be Markovian, i.e., memoryless. We characterize these non-Markovian dynamics and show how this influences the dynamics of clusters during nucleation. Our results are validated by simulations of a three-dimensional Ising model with locally conserved magnetization.