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Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations

  • 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.

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Author:Peter Dieterich, Rainer Klages, Aleksei V. ChechkinORCiDGND
ISSN:1367-2630 (print)
Parent Title (English):New journal of physics : the open-access journal for physics
Publisher:IOP Publ. Ltd.
Place of publication:Bristol
Document Type:Article
Year of first Publication:2015
Year of Completion:2015
Release Date:2017/03/27
Tag:Fokker-Planck equations; anomalous diffusion; fluctuation relations; stochastic processes; stochastic thermodynamics
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Publication Way:Open Access