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Tsallis distributions, Lévy walks and correlated-type anomalous diffusion result from state-dependent diffusion

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  • Reynolds, A.M.
  • Geritz, S.A.H.

Abstract

We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (q-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic movements), Lévy walks and multiplicative noise. Our analyses find empirical support in the movements of single Hydra and kidney cells in cell aggregates. It may explain why Tsallis distributions characterise seemingly disparate phenomena including cell motility, inverse bremsstrahlung absorption, high-energy particle collisions, particle movements in granular matter and the re-association of heme-ligands in folded proteins. The common underlining factor is state-dependent diffusion.

Suggested Citation

  • Reynolds, A.M. & Geritz, S.A.H., 2015. "Tsallis distributions, Lévy walks and correlated-type anomalous diffusion result from state-dependent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 317-321.
    • Handle: RePEc:eee:phsmap:v:424:y:2015:i:c:p:317-321
    DOI: 10.1016/j.physa.2015.01.034
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    Cited by:

    1. Sakiyama, T. & Gunji, Y.P., 2015. "Weber–Fechner relation and Lévy-like searching stemmed from ambiguous experiences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 161-168.

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