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.
Author details: | Peter Dieterich, Rainer KlagesORCiDGND, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/17/7/075004 |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Tag: | Fokker-Planck equations; anomalous diffusion; fluctuation relations; stochastic processes; stochastic thermodynamics |
Volume: | 17 |
Number of pages: | 14 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |
Publishing method: | Open Access |