Global ETD Search

1	Symmetric Fractional Diffusion and Entropy Production Prehl, Janett, Boldt, Frank, Hoffmann, Karl Heinz, Essex, Christopher 30 August 2016 (has links) (PDF) 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. Entropieproduktionsparadox Pseudopropagation Symmetrische fraktionale Diffusion Stabile Verteilungen Technische Universität Chemnitz Publikationsfonds fractional diffusion entropy production paradox pseudo propagation symmetric fractional diffusion Technische Universität Chemnitz Publication fund ddc:500 Diffusionsgleichung Entropie Ableitung gebrochener Ordnung
2	Symmetric Fractional Diffusion and Entropy Production Prehl, Janett, Boldt, Frank, Hoffmann, Karl Heinz, Essex, Christopher 30 August 2016 (has links) 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. info:eu-repo/classification/ddc/500 ddc:500
3	Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime Hoffmann, Karl Heinz, Kulmus, Kathrin, Essex, Christopher, Prehl, Janett 13 February 2019 (has links) The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation. info:eu-repo/classification/ddc/530 ddc:530 info:eu-repo/classification/ddc/510 ddc:510 Diffusion; Entropie

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