Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 27: Transport and Anomalous Diffusion
DY 27.4: Talk
Thursday, March 29, 2012, 15:30–15:45, MA 004
The resolution of the entropy production paradox of fractional diffusion equations — •Janett Prehl1, Karl Heinz Hoffmann1, and Chris Essex2 — 1TU Chemnitz, Institut für Physik, D-09107 Chemnitz, Germany — 2University of Western Ontario, Departement of Applied Mathematics, London, ON, Canada N6A 5B7
Both, time- and space-fractional diffusion equations can be defined as a one parameter bridging regime going from diffusion equation to wave- or half wave equation. The solutions of these fractional diffusion equations represent superdiffusion processes. Contrary to intuition, the corresponding entropy production rates grow moving from irreversible diffusive to reversible wave-like behavior. This paradox was discovered for the time- and space-fractional diffusion equation and not only for the Shannon entropy but also for its generalized entropy definitions, the Tsallis and the Rényi entropy. For the first time we show a generalized method to resolve this paradoxical behavior for both fractional equations and all introduced entropy definitions.
[1] C. Essex, C. Schulzky, A. Franz, K. H. Hoffmann, Phys,A (2000) 284: 299–309
[2] J. Prehl, C. Essex, K. H. Hoffmann, Phys.A (2010) 389: 215–224