Incidence of q statistics in rank distributions

Yalcin G. Ç., Robledo A., Gell-Mann M.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, vol.111, no.39, pp.14082-14087, 2014 (SCI-Expanded) identifier identifier identifier


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.