ArticleProceedings of the National Academy of Sciences of the United States of America2013
A maximum entropy framework for nonexponential distributions.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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Who cites it
14 citing papers in PubMed.
- Discovering interpretable low-dimensional dynamics using maximum entropy.Physical review. E · 2026Article
- Exploring Numerical Correlations: Models and Thermodynamic Kappa.Entropy (Basel, Switzerland) · 2025Article
- Correlations and Kappa Distributions: Numerical Experiment and Physical Understanding.Entropy (Basel, Switzerland) · 2025Article
- The theory of thermodynamic relativity.Scientific reports · 2024Article
- Effect of contact inhibition locomotion on confined cellular organization.Scientific reports · 2023Article
- Entropy defect in thermodynamics.Scientific reports · 2023Article
- The Maximum Caliber Variational Principle for Nonequilibria.Annual review of physical chemistry · 2020Review
- From Boltzmann to Zipf through Shannon and Jaynes.Entropy (Basel, Switzerland) · 2020Article
- Relating Vertex and Global Graph Entropy in Randomly Generated Graphs.Entropy (Basel, Switzerland) · 2018Article
- Large-Scale Analysis of Zipf's Law in English Texts.PloS one · 2016Article
- Memoryless self-reinforcing directionality in endosomal active transport within living cells.Nature materials · 2015Article
- Predictability of extreme events in social media.PloS one · 2014Article
- Universal internucleotide statistics in full genomes: a footprint of the DNA structure and packaging?PloS one · 2014Article
- Article
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Authors and funding
3 authors.
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Abstract
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions for situations in which a "joiner particle" k pays some form of price to enter a community of size , where costs are subject to economies of scale. Maximizing the Boltzmann-Gibbs-Shannon entropy subject to this energy-like constraint predicts a distribution having a power-law tail; it reduces to the Boltzmann distribution in the absence of economies of scale. We show that the predicted function gives excellent fits to 13 different distribution functions, ranging from friendship links in social networks, to protein-protein interactions, to the severity of terrorist attacks. This approach may give useful insights into when to expect power-law distributions in the natural and social sciences.
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