Information entropy of classical versus explosive percolation

TL;DR

This paper compares the Shannon entropy of cluster size distributions in classical and explosive percolation, revealing differences in entropy behavior at critical points and proposing a new method to identify criticality through entropy derivatives.

Contribution

It introduces an entropy-based analysis of percolation, showing how entropy behavior differs between classical and explosive types and offering a novel way to locate critical points.

Findings

Entropy peaks at classical percolation critical point

Explosive percolation entropy peak does not match the critical point

Critical points can be identified via entropy derivatives

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.