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Symmetric Fractional Diffusion and Entropy Production

by Janett Prehl 1,†, Frank Boldt 1,†, Karl Heinz Hoffmann 1,*,† and Christopher Essex 2,†
Institut für Physik, Technische Universität Chemnitz, Chemnitz D-09107, Germany
Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Kevin H. Knuth
Entropy 2016, 18(7), 275;
Received: 3 June 2016 / Revised: 15 July 2016 / Accepted: 20 July 2016 / Published: 23 July 2016
(This article belongs to the Section Thermodynamics)
The discovery of the entropy production paradox (Hoffmann et al., 1998) raised basic questions about the nature of irreversibility in the regime between diffusion and waves. First studied in the form of spatial movements of moments of H functions, pseudo propagation is the pre-limit propagation-like movements of skewed probability density function (PDFs) in the domain between the wave and diffusion equations that goes over to classical partial differential equation propagation of characteristics in the wave limit. Many of the strange properties that occur in this extraordinary regime were thought to be connected in some manner to this form of proto-movement. This paper eliminates pseudo propagation by employing a similar evolution equation that imposes spatial unimodal symmetry on evolving PDFs. Contrary to initial expectations, familiar peculiarities emerge despite the imposed symmetry, but they have a distinct character. View Full-Text
Keywords: fractional diffusion; entropy production paradox; pseudo propagation; symmetric fractional diffusion fractional diffusion; entropy production paradox; pseudo propagation; symmetric fractional diffusion
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Prehl, J.; Boldt, F.; Hoffmann, K.H.; Essex, C. Symmetric Fractional Diffusion and Entropy Production. Entropy 2016, 18, 275.

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