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Open AccessArticle

A Maximum Entropy Method for the Prediction of Size Distributions

by Cornelia Metzig 1,2,* and Caroline Colijn 3,4
1
Business School, Imperial College London, London SW7 2AZ, UK
2
School of Electronic Engineering and Computer Science, Queen Mary University, London E1 7NS, UK
3
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
4
Department of Mathematics, Simon Fraser University, Surrey, BC V3T0A3, Canada
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 312; https://doi.org/10.3390/e22030312
Received: 5 November 2019 / Revised: 16 February 2020 / Accepted: 5 March 2020 / Published: 10 March 2020
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of constant size, which contains exit of balls and urns (or nodes and edges for the network case). Knowing mean size (degree) and turnover rate, the power law exponent and exponential cutoff can be derived. Our results are confirmed by simulations and by computation of exact probabilities. We also apply this entropy method to reproduce existing results like the Maxwell-Boltzmann distribution for the velocity of gas particles, the Barabasi-Albert model and multiplicative noise systems. View Full-Text
Keywords: complex networks; growth process; fluctuation scaling; Gibbs-Shannon entropy; scalefree distribution complex networks; growth process; fluctuation scaling; Gibbs-Shannon entropy; scalefree distribution
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Metzig, C.; Colijn, C. A Maximum Entropy Method for the Prediction of Size Distributions. Entropy 2020, 22, 312.

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