The European Physical Journal Special Topics

, Volume 143, Issue 1, pp 209–215 | Cite as

Generalized diffusion and pretransitional fluctuations statistics

  • J.-P. Boon
  • P. Grosfils
  • J. F. Lutsko


(a) For diffusion type processes, non-Gaussian distributions are obtained, in a generic manner, from a generalization of classical linear response theory; (b) Statistical properties of hydrodynamic fields reveal pretransitional fluctuations in fingering processes, and these precursors are found to exhibit power law distributions; (c) These power laws are shown to follow from q-Gaussian structures which are solutions to the generalized diffusion equation. The present analysis (i) offers a physical picture of the precursors dynamics, (ii) suggests a physical interpretation of nonextensivity from the structure of the precursors, and (iii) provides an illustration of the emergence of statistics from dynamics.


Vorticity European Physical Journal Special Topic Porous Media Equation Classical Statistical Mechanic Lattice Boltzmann Equation 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • J.-P. Boon
    • 1
  • P. Grosfils
    • 2
  • J. F. Lutsko
    • 1
  1. 1.Physics Department, CP 231Université Libre de BruxellesBruxellesBelgium
  2. 2.Chimie Physique, E.P. CP 165/62, Université Libre de BruxellesBruxellesBelgium

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