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

  • Ubriaco M
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Abstract

Starting with the relative entropy based on a previously proposed entropy function Sqp=int dx 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 qto 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 sim K 1/qt 1/q, where the parameter q takes values q=frac2n-12n+1 (superdiffusion) and q=frac2n+12n-1 (subdiffusion), forall ngeq 1.

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Authors

  • Marcelo R. Ubriaco

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