A simple mathematical model for anomalous diffusion via Fisher's information theory

  • Ubriaco M
  • 0

    Readers

    Mendeley users who have this article in their library.
  • 11

    Citations

    Citations of this article.

Abstract

Starting with the relative entropy based on a previously proposed entropy function Sq [p] = ∫ d x p (x) × (- ln p (x))q, we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher information measure with respect to the new function and obtain a differential operator that reduces to a space coordinate second derivative in the q → 1 limit. We then propose a simple differential equation for anomalous diffusion and show that its solutions are a generalization of the functions in the Barenblatt-Pattle solution. We find that the mean squared displacement, up to a q-dependent constant, has a time dependence according to 〈 x2 〉 ∼ K1 / q t1 / q, where the parameter q takes values q = frac(2 n - 1, 2 n + 1) (superdiffusion) and q = frac(2 n + 1, 2 n - 1) (subdiffusion), ∀ n ≥ 1. © 2009 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Anomalous diffusion
  • Entropy
  • Fisher information

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free