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

We show that the use of the recently proposed thermostatistics based o n the generalized entropic form S-q = k(1 - Sigma(i) Pi(q))/(q - 1) (w here q is an element of R, with q = 1 corresponding to the Boltzmann-G ibbs-Shannon entropy -k Sigma(i) pi ln pi), together with the Levy-Gne denko generalization of the central limit theorem, provide a basic ste p towards the understanding of why Levy distributions are ubiquitous i n nature. A consistent experimental verification is proposed.