Information entropy of classical versus explosive percolation

Abstract

We study the Shannon entropy of the cluster size distribution in classical as well as explosive percolation, in order to estimate the uncertainty in the sizes of randomly chosen clusters. At the critical point the cluster size distribution is a power-law, i.e. there are clusters of all sizes, so one expects the information entropy to attain a maximum. As expected, our results show that the entropy attains a maximum at this point for classical percolation. Surprisingly, for explosive percolation the maximum entropy does not match the critical point. Moreover, we show that it is possible determine the critical point without using the conventional order parameter, just analysing the entropy's derivatives.