Nonextensive Statistical Mechanics, Anomalous Diffusion and Central Limit Theorems |
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Authors: | Constantino Tsallis |
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Institution: | (1) Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA;(2) Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil |
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Abstract: | We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations
and with existing central limit theorems. We then provide some hints that might pave the road to the proof of a new central
limit theorem, which would play a fundamental role in the foundations and ubiquity of nonextensive statistical mechanics.
The basic novelty introduced within this conjectural theorem is the generalization of the hypothesis of independence of the N random variables being summed. In addition to this, we also advance some nonlinear dynamical (possibly exact) relations which
generalize the concepts of Lyapunov exponents, entropy production per unit time, and their interconnection as first proved
by Pesin for chaotic systems.
The article is available online on SpringerLink (www.springerlink.com) using colors instead of greyscales in Figure 4.1.
Lecture held in the Seminario Matematico e Fisico on May 21, 2004 Received: December 2004 |
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