Effect of time delay on feedback control of a flashing ratchet

It was recently shown that the use of feedback control can improve the performance of a flashing ratchet. We investigate the effect of a time delay in the implementation of feedback control in a closed-loop collective flashing ratchet, using Langevin dynamics simulations. Surprisingly, for a large ensemble, a well-chosen delay time improves the ratchet performance by allowing the system to synchronize into a quasi-periodic stable mode of oscillation that reproduces the optimal average velocity for a periodically flashing ratchet. For a small ensemble, on the other hand, finite delay times significantly reduce the benefit of feedback control for the time-averaged velocity, because the relevance of information decays on a time scale set by the diffusion time of the particles. Based on these results, we establish that experimental use of feedback control is realistic.Comment: 6 pages, 6 figures, to appear in Europhysics Letter

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.Comment: 4 pages, 4 figure

Extracting work optimally with imprecise measurements

Measurement and feedback allows an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally even with a high degree of inaccuracy in the measurements.Comment: 13 pages, 6 figures. Published in Entropy (open access

Efficiency of Brownian Motors

The efficiency of different types of Brownian motors is calculated analytically and numerically. We find that motors based on flashing ratchets present a low efficiency and an unavoidable entropy production. On the other hand, a certain class of motors based on adiabatically changing potentials, named reversible ratchets, exhibit a higher efficiency and the entropy production can be arbitrarily reduced.Comment: LaTeX 209, 6 pages, 7 postscript figures, uses psfi

Deterministic ratchet from stationary light fields

Ratchets are dynamic systems where particle transport is induced by zero-average forces due to the interplay between nonlinearity and asymmetry. Generally, they rely on the effect of a strong external driving. We show that stationary optical lattices can be designed to generate particle flow in one direction while requiring neither noise nor driving. Such optical fields must be arranged to yield a combination of conservative (dipole) and nonconservative (radiation pressure) forces. Under strong friction all paths converge to a discrete set of limit periodic trajectories flowing in the same direction.Comment: 6 pages, 4 figure