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Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics

  • Part 4: Lévy Flights and Statistical Mechanics
  • Conference paper
  • First Online:
Lévy Flights and Related Topics in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 450))

Abstract

The robustness and ubiquity of the macroscopic normal diffusion is well known to be derivable within Boltzmann-Gibbs statistical mechanics. It is essentially founded on (i) a variational principle applied to S = − f dxp(x)ln[p(x)] with simple a priori constraints, and (ii) the central limit theorem. Its basic characterization consists in the time evolution < x2 > ∝ t. A recently generalized statistical mechanics enables the extension of the same program in order to also cover the long-tail Lévy-like anomalous superdiffusion, a phenomenon frequently encountered in Nature. By so doing, this formalism succeeds where standard statistical mechanics and thermodynamics are known to fail.

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Author information

Authors and Affiliations

  1. Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, 48824-1116, East Lansing, Michigan, USA

    Constantino Tsallis

  2. Centeo Brasileiro de Pesquisas Físicas/CNPq, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ, Brazil

    Constantino Tsallis & André M. C. de Souza

  3. Departamento de Fésica, Univeisidade Federal de Sergipe, 49000-000, Aracaju-SE, Brazil

    André M. C. de Souza

  4. Laboratoire d'Expérimentation Numérique, Maison des Magistères-CNRS, B.P. 166, 38042, Grenoble Cedex 9, France

    Roger Maynard

Authors
  1. Constantino Tsallis
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  2. André M. C. de Souza
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  3. Roger Maynard
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Micheal F. Shlesinger George M. Zaslavsky Uriel Frisch

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© 1995 Springer-Verlag

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Tsallis, C., de Souza, A.M.C., Maynard, R. (1995). Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics. In: Shlesinger, M.F., Zaslavsky, G.M., Frisch, U. (eds) Lévy Flights and Related Topics in Physics. Lecture Notes in Physics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59222-9_40

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  • DOI: https://doi.org/10.1007/3-540-59222-9_40

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  • Print ISBN: 978-3-540-59222-8

  • Online ISBN: 978-3-540-49225-2

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