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 - TY - JOUR A1 - Goychuk, I. A1 - Kharchenko, V. O. T1 - Rocking subdiffusive ratchets origin, optimization and efficiency JF - Mathematical modelling of natural phenomena N2 - We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale. KW - anomalous Brownian motion KW - generalized Langevin equation KW - memory effects KW - viscoelasticity KW - ratchet transport KW - stochastic thermodynamics Y1 - 2013 U6 - https://doi.org/10.1051/mmnp/20138210 SN - 0973-5348 VL - 8 IS - 2 SP - 144 EP - 158 PB - EDP Sciences CY - Les Ulis ER -