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Entropy 2016, 18(7), 275; doi:10.3390/e18070275

Symmetric Fractional Diffusion and Entropy Production

1
Institut für Physik, Technische Universität Chemnitz, Chemnitz D-09107, Germany
2
Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 3 June 2016 / Revised: 15 July 2016 / Accepted: 20 July 2016 / Published: 23 July 2016
(This article belongs to the Section Thermodynamics)
View Full-Text   |   Download PDF [474 KB, uploaded 23 July 2016]   |  

Abstract

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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Prehl, J.; Boldt, F.; Hoffmann, K.H.; Essex, C. Symmetric Fractional Diffusion and Entropy Production. Entropy 2016, 18, 275.

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