Feedback Control in a Collective Flashing Ratchet

Abstract

An ensemble of Brownian particles in a feedback controlled flashing ratchet is studied. The ratchet potential is switched on and off depending on the position of the particles, with the aim of maximizing the current. We study in detail a protocol which maximizes the instant velocity of the center of mass of the ensemble at any time. This protocol is optimal for one particle and performs better than any periodic flashing for ensembles of moderate size, but is defeated by a random or periodic switching for large ensembles.

Information and flux in a feedback controlled Brownian ratchet

“…4, we also discuss the performance of the feedback ratchet as a function of the correlation established between the controlled system and the controller, and briefly discuss other performance measures for feedback ratchets, including the power output and the thermodynamic efficiency. The results that we obtain are in the end specific to the feedback ratchet of [6], but the method that we describe, which is inspired from Maxwell's concept of thermodynamic demons [13], information theory [14] and the work of one of us [15], is general and can be applied to other feedback ratchets and other control systems.…”

“…This feedback flashing ratchet could be implemented experimentally by monitoring colloidal particles suspended in solution and by exposing the particles to a saw-tooth dielectric potential as in [9], but with the potential turned on and off depending on particles' state. The feedback ratchet of [6] has also been proposed as a mechanism to explain the stepping motion of a two-headed motor protein [10]. In a more general context, recent experiments have shown that information about the location of a macrocycle in a rotaxane-an organic molecule with a ring threaded onto an axle-can be used to induce direct transport away from thermal equilibrium [11].…”

“…An example of closed-loop ratchet based on the flashing ratchet was proposed in [6] (see also [7]). This feedback flashing ratchet could be implemented experimentally by monitoring colloidal particles suspended in solution and by exposing the particles to a saw-tooth dielectric potential as in [9], but with the potential turned on and off depending on particles' state.…”

“…Thermal ratchets or Brownian motors can be viewed as controllers that act on stochastic systems with the aim of inducing directed motion through the rectification of fluctuations [1,2,3,4,5,6,7]. In most cases, the system to be controlled is modelled as a collection of Brownian particles undergoing Langevin dynamics, and the control action-that is, the rectification mechanism-is implemented by applying random or deterministic time-dependent perturbations to the particles.…”

“…Our goal in this paper is to establish a quantitative comparison between closed-and open-loop ratchets that explicitly focuses on what distinguishes them, namely the use of information. This is done in three steps using the feedback ratchet of [6] as a case example. First, we show how the information used by this ratchet can be quantified (Sec.…”