Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 111, Issue 39, Pages 14082-14087Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1412093111
Keywords
rank-ordered data; generalized entropies
Categories
Funding
- Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico [IN100311]
- Consejo Nacional de Ciencia y Technologia [CB-2011-167978]
- Scientific Research Projects Coordination Unit of Istanbul University [36529]
- Insight Venture Partners
- Bryan J. and June B. Zwan Foundation
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We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. Whereas the value of the index a fixes the distribution's power-law exponent, that for the dual index 2 - alpha ensures the extensivity of the deformed entropy.
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