A simple mathematical model for anomalous diffusion via Fisher's information theory |
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Authors: | Marcelo R Ubriaco |
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Institution: | Laboratory of Theoretical Physics, Department of Physics, University of Puerto Rico, Río Piedras Campus, San Juan, PR 00931, USA |
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Abstract: | Starting with the relative entropy based on a previously proposed entropy function , 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/qt1/q, where the parameter q takes values (superdiffusion) and (subdiffusion), ∀n?1. |
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Keywords: | 89 70 Cf 05 20 -y |
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