TY  - JOUR
A1  - Dieterich, Peter
A1  - Klages, Rainer
A1  - Chechkin, Aleksei V.
T1  - Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
JF  - New journal of physics : the open-access journal for physics
N2  - 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.
KW  - fluctuation relations
KW  - anomalous diffusion
KW  - stochastic processes
KW  - stochastic thermodynamics
KW  - Fokker-Planck equations
Y1  - 2015
U6  - https://doi.org/10.1088/1367-2630/17/7/075004
SN  - 1367-2630
VL  - 17
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -