Generalized diffusion and pretransitional fluctuations statistics
Physics Department, CP 231, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
2 Chimie Physique, E.P. CP 165/62, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
(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.
© EDP Sciences, Springer-Verlag, 2007