Regensburg 2016 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 61: Anomalous Diffusion in Complex Environments (Focus Session)
BP 61.5: Vortrag
Donnerstag, 10. März 2016, 12:30–12:45, H45
Fluctuation relations for anomalous dynamics generated by time fractional Fokker-Planck equations — Peter Dieterich1, •Rainer Klages2,3, and Aleksei V. Chechkin2,4,5 — 1Institut fuer Physiologie, Technische Universitaet Dresden — 2Max Planck Institute for the Physics of Complex Systems, Dresden — 3Queen Mary University of London, School of Mathematical Sciences — 4Institute for Theoretical Physics NSC KIPT, Kharkov, Ukraine — 5Institute of Physics and Astronomy, University of Potsdam
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super- and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not.We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work.We discuss possible applications of these types of dynamics and FRs to experiments.
P. Dieterich et al., New J. Phys. 17, 075004 (2015)