Statistical-mechanical foundation of the ubiquity of lévy distributions in nature

Abstract

We show that the use of the recently proposed thermostatistics based on the generalized entropic form Sqk(1-ipiq)(q-1) (where qR, with q=1 corresponding to the Boltzmann-Gibbs-Shannon entropy -kipilnpi), together with the Lévy-Gnedenko generalization of the central limit theorem, provide a basic step towards the understanding of why Lévy distributions are ubiquitous in nature. A consistent experimental verification is proposed. © 1995 The American Physical Society.