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_kassociated with the ensemble of clusters consisting of k particles is determined for diffusion-limited aggregates (DLA) and Eden clusters using the expression S_k = - ∑ P_iln (p_i)/k, where p_i is the probability for the i-th configuration to occur. The expressions S = limS_k 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.