Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 110, Issue 51, Pages 20380-20385Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1320578110
Keywords
heavy tail; fat tail; statistical mechanics; thermostatistics; social physics
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Funding
- US Department of Defense National Defense Science and Engineering Graduate Fellowship
- National Science Foundation and Laufer Center
- Department of Energy Grant from the Office of Biological Research [PM-031]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1205881] Funding Source: National Science Foundation
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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 {pk} for situations in which a joiner particle k pays some form of price to enter a community of size k-1, 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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