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Abstract
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.