STATISTICAL-MECHANICAL FOUNDATION OF THE UBIQUITY OF LEVY DISTRIBUTIONS IN NATURE

We show that the use of the recently proposed thermostatistics based on the generalized entropic form S-q = k(1 - Sigma(i) Pi(q))/(q - 1) (where q is an element of R, with q = 1 corresponding to the Boltzmann-Gibbs-Shannon entropy -k Sigma(i) pi ln pi), together with the Levy-Gnedenko generalization of the central limit theorem, provide a basic step towards the understanding of why Levy distributions are ubiquitous in nature. A consistent experimental verification is proposed.