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.

6 pages, 6 figures

References in corpus (5)

• Recent advances in percolation theory and its applications
• Explosive percolation via control of the largest cluster
• Recent advances and open challenges in percolation
• Solution of the explosive percolation quest: Scaling functions and critical exponents
• Critical exponents of the explosive percolation transition

Cited by in corpus (6)

• On entropy, specific heat, susceptibility and Rushbrooke inequality in percolation
• Product-Sum universality and Rushbrooke inequality in explosive percolation
• Scaling behavior of information entropy in explosive percolation transitions
• Redefinition of site percolation in light of entropy and the second law of thermodynamics
• Universality class of explosive percolation in Barabási-Albert networks
• Thermodynamic analysis of diverse percolation transitions