Eur. Phys. J. B (2015) 88: 213
https://doi.org/10.1140/epjb/e2015-60500-0

Regular Article

Information entropy of classical versus explosive percolation

¹ Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, Rio Grande do Norte, Brazil
² National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, Rio Grande do Norte, Brazil

^a e-mail: tiagotmv@gmail.com

Received: 28 April 2015
Received in final form: 24 June 2015
Published online: 2 September 2015

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 to determine the critical point without using the conventional order parameter, just analysing the entropy’s derivatives.