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, Skassociated with the ensemble of clusters consisting of k particles is determined for diffusion-limited aggregates (DLA) and Eden clusters using the expression Sk = - ∑ Piln (pi)/k, where pi is the probability for the i-th configuration to occur. The expressions S = limSk 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)