Dresden 2014 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

DY: Fachverband Dynamik und Statistische Physik

DY 4: Anomalous Diffusion

DY 4.5: Vortrag

Montag, 31. März 2014, 10:30–10:45, ZEU 146

Relative entropies and anomalous diffusion — •Janett Prehl¹, Frank Boldt¹, Christopher Essex², and Karl Heinz Hoffmann¹ — ¹Technische Universität Chemnitz, Institut of Physics, Chemnitz, Germany — ²University of Western Ontario, Department of Applied Mathematics, London, Canada

The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly [1]. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all [1]. In this talk we will present that different to entropies and entropy production rates relative entropies, with an appropriately chosen reference distribution, will order the bridging regime [2]. Thus, they provide a physically sensible way of setting which process is “nearer” to pure diffusion than another, placing pure wave propagation, desirably, “furthest” from pure diffusion. Furthermore, we examine the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives [3].
[1] K.H. Hoffmann et al., J. Non-Equilib. Thermodyn. 37, 393 (2012)

[2] J. Prehl et al., Entropy 14, 701 (2012)

[3] J. Prehl et al., Entropy 15, 2989 (2013)