title: Incidence of q statistics in rank distributions.
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.
authors.affiliation: Department of Physics, Istanbul University, Vezneciler, Istanbul 34134, Turkey;
authors.forename: G Cigdem
authors.initials: GC
authors.lastname: Yalcin
authors.affiliation: Instituto de Fisica y Centro de Ciencias de la Complejidad, Universidad Nacional Autonoma de Mexico, 01000 Mexico D.F., Mexico; and.
authors.forename: Alberto
authors.initials: A
authors.lastname: Robledo
authors.affiliation: Santa Fe Institute, Santa Fe, NM 87501 mgm@santafe.edu.
authors.forename: Murray
authors.initials: M
authors.lastname: Gell-Mann
keywords: generalized entropies; rank-ordered data