Realization of a Feedback Controlled Flashing Ratchet

López, Benjamín; Kuwada, Nathan J.; Craig, Erin M.; Long, Brian; Linke, Heiner

doi:10.1103/physrevlett.101.220601

Cited by 112 publications

(130 citation statements)

References 17 publications

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“…This is in contrast to previous studies using Langevin equations [10,19,30] where the dynamical variable is the particle position itself. Second, the mean position is an experimentally accessible quantity, which can be monitored, e.g., by video microscopy [19].…”

Section: Definition Of the Modelcontrasting

confidence: 48%

“…This is different from earlier studies based on the Langevin equation (see, e.g., [10,19,30]), where the feedback is applied directly to the position of one particle, χ i (t), or to the average of N particle positions…”

Section: Transport Mechanismmentioning

confidence: 76%

“…It has been shown that feedback control can lead to pronounced changes of the dynamics compared to purely external ("open-loop") control and can, in some cases, strongly improve transport properties such as effective currents. A prime example from the classical side are ratchet systems (or Brownian motors) [5,6], specifically the so-called flashing ratchets that operate by switching on and off a spatially periodic asymmetric potential: here it has been shown, both theoretically [7][8][9] and experimentally [10], that the fluctuationinduced directed transport can be strongly enhanced by switching not under an externally defined protocol, but "on demand". Besides the dynamics itself, another topic of intense research is the impact of feedback control on non-equilibrium thermodynamics [3,11,12], concerning particularly the entropy production and fluctuation theorems in both, classical [11,13] and quantum systems [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we model V (z) by a periodic, piecewise linear, "sawtooth" potential [10,37,38] defined by V (z + L) = V (z) and…”

Section: Definition Of the Modelmentioning

confidence: 99%

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Delay-induced transport in a rocking ratchet under feedback control

2014

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Based on the Fokker-Planck equation we investigate the transport of an overdamped colloidal particle in a static, asymmetric periodic potential supplemented by a time-dependent, delayed feedback force, F fc . For a given time t, F fc depends on the status of the system at a previous time t − τD, with τD being a delay time, specifically on the delayed mean particle displacement (relative to some "switching position"). For non-zero delay times F fc (t) develops nearly regular oscillations generating a net current in the system. Depending on the switching position, this current is nearly as large or even larger than that in a conventional open-loop rocking ratchet. We also investigate thermodynamic properties of the delayed non-equilibrium system and we suggest an underlying Langevin equation which reproduces the Fokker-Planck results.

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Section: Definition Of the Modelcontrasting

confidence: 48%

Section: Transport Mechanismmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

“…In the present paper we model V (z) by a periodic, piecewise linear, "sawtooth" potential [10,37,38] defined by V (z + L) = V (z) and…”

Section: Definition Of the Modelmentioning

confidence: 99%

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Delay-induced transport in a rocking ratchet under feedback control

2014

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“…In fact, stochastic violations of the second law have been observed 11,12 ; nonetheless, the second law still holds, on average, if the initial state is in thermal equilibrium: F −W ≤ 0, where F is the free-energy difference between states, W the work done on the system and · the ensemble average. However, the feedback control enables us to selectively manipulate only fluctuations that cause F − W > 0 such as upward jumps by using the information about the system [13][14][15] . Here, 'feedback' means that control protocols depend on measurement outcomes of the controlled system, in other words, 'feedback control' means a 'closed-loop control' 16 .…”

mentioning

confidence: 99%

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

et al. 2010

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In 1929, Leó Szilárd invented a feedback protocol 1 in which a hypothetical intelligence-dubbed Maxwell's demon-pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy 2-6 . An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using realtime feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality 7 , and suggests a new fundamental principle of an 'information-to-heat engine' that converts information into energy by feedback control.To illustrate the basic idea of our feedback protocol, let us consider a microscopic particle on a spiral-staircase-like potential ( Fig. 1). We set the height of each step comparable to the thermal energy k B T , where k B is the Boltzmann constant and T is temperature. Subjected to thermal fluctuations, the particle jumps between steps stochastically. Although the particle sometimes jumps to an upper step, downward jumps along the gradient are more frequent than upward jumps. In this manner, on average, the particle falls down the stairs unless it is externally pushed up (Fig. 1a). Now, let us consider the following feedback control: We measure the particle's position at regular intervals, and if an upward jump is observed we place a block behind the particle to prevent subsequent downward jumps (Fig. 1b). If this procedure is repeated, the particle is expected to climb up the stairs. Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. In such a case, what drives the particle to climb up the stairs? This apparent contradiction to the second law of thermodynamics, epitomized by Maxwell's demon, inspired many physicists to generalize the principles of thermodynamics 1,5,6 . It is now understood that the particle is driven by the 'information' gained by the measurement of the particle's location 5,8 .In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant but particle on a spiral-staircase-like potential with a step height comparable to k B T. The particle stochastically jumps between steps owing to thermal fluctuations. As the downward jumps along the gradient are more frequent than the upward ones, the particle falls down the stairs, on average. b, Feedback control. When an upward jump is observed, a block is placed behind the particle to prevent downward jumps. By repeating ...

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Information Thermodynamics: Maxwell's Demon in Nonequilibrium Dynamics

Sagawa

Ueda

2013

Nonequilibrium Statistical Physics of Small Systems

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We review theory of information thermodynamics which incorporates effects of measurement and feedback into nonequilibrium thermodynamics of a small system, and discuss how the second law of thermodynamics should be extended for such situations. We address the issue of the maximum work that can be extracted from the system in the presence of a feedback controller (Maxwell's demon) and provide a few illustrative examples. We also review a recent experiment that realized a Maxwell's demon based on a feedback-controlled ratchet.

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Realization of a Feedback Controlled Flashing Ratchet

Cited by 112 publications

References 17 publications

Delay-induced transport in a rocking ratchet under feedback control

Delay-induced transport in a rocking ratchet under feedback control

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

Information Thermodynamics: Maxwell's Demon in Nonequilibrium Dynamics

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