Bibliographic Details
| Title: |
Incidence of q statistics in rank distributions. |
| Authors: |
Yalcin, G. Cigdem1, Robledo, Alberto2, Gell-Mann, Murray3 mgm@santafe.edu |
| Source: |
Proceedings of the National Academy of Sciences of the United States of America. 9/30/2014, Vol. 111 Issue 39, p14082-14087. 6p. |
| Subjects: |
Lyapunov exponents, Numerical solutions to differential equations, Bifurcation theory, Stability (Mechanics), Entropy |
| Abstract: |
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 α fixes the distribution's power-law exponent, that for the dual index 2 - α ensures the extensivity of the deformed entropy. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
