Distribution and Entropy of Clusters in Growth Models

We introduce a new approach to the description of cluster statistics in growth models by calculating the entropy of clusters from the probability distribution in their phase space. The entropy, S k , associated with the ensemble of clusters consisting of k particles is determined for diffusion-limited aggregates (DLA) and Eden clusters using the expression S k = - Σ p i ln( p i )/ k , where p i is the probability for the i -th configuration to occur. The expressions provides a new characteristic quantity of the growth processes, in addition to the widely used fractal dimension. Our simulations on the square lattice give S (DLA) = 1.3 ± 0.1 and S (Eden) = 1.1 ± 0.1. The results are compared with the entropies of clusters calculated for equilibrium models.