Open Problems on Information and Feedback Controlled Systems

Cao, Francisco J.; Feito, M.

doi:10.3390/e14040834

Cited by 14 publications

(19 citation statements)

References 57 publications

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“…As discussed in several studies (see, e.g., Refs. [8,9,[19][20][21][22]), time delay is a rather natural phenomenon which may arise, e.g., through the finite time required for measuring or processing information from a measurement. In the present case, as we will demonstrate below, the time delay is indeed crucial for generating particle transport.…”

Section: Definition Of the Modelmentioning

confidence: 99%

“…Whereas many earlier studies of feedback-controlled systems focused on instantaneous feedback (i.e., no time lag between measurement and control action) [7,18], there is increasing interest in exploring systems with time delay [8,9,[19][20][21][22]. The latter typically arises from a time lag between the detection of a signal and the control action, an essentially omnipresent situation in experimental setups.…”

Section: Introductionmentioning

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 Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delay-induced transport in a rocking ratchet under feedback control

2014

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“…To calculate W info we transform the data for F ext (t) (figure 4(b)) obtained from Langevin simulations into a binary string, representing changes in the direction of the force as '1' and unchanged force as '0', and calculate the probability p of motor reversals as the number of switches divided by the number of half-cycles. The information cost can then be determined from the Shannon entropy [39] as…”

Section: Input Energymentioning

confidence: 99%

“…info This represents an upper limit to the information cost, which is exact for completely uncorrelated force switching times. If the switching probability were 50%, W info would reach a maximum kTln2 per step, which is known as the Landauer limit for information [39,40].…”

Section: Input Energymentioning

confidence: 99%

Motor properties from persistence: a linear molecular walker lacking spatial and temporal asymmetry

et al. 2015

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The stepping direction of linear molecular motors is usually defined by a spatial asymmetry of the motor, its track, or both. Here we present a model for a molecular walker that undergoes biased directional motion along a symmetric track in the presence of a temporally symmetric chemical cycle. Instead of using asymmetry, directionality is achieved by persistence. At small load force the walker can take on average thousands of steps in a given direction until it stochastically reverses direction. We discuss a specific experimental implementation of a synthetic motor based on this design and find, using Langevin and Monte Carlo simulations, that a realistic walker can work against load forces on the order of picoNewtons with an efficiency of ∼18%, comparable to that of kinesin. In principle, the walker can be turned into a permanent motor by externally monitoring the walker's momentary direction of motion, and using feedback to adjust the direction of a load force. We calculate the thermodynamic cost of using feedback to enhance motor performance in terms of the Shannon entropy, and find that it reduces the efficiency of a realistic motor only marginally. We discuss the implications for natural protein motor performance in the context of the strong performance of this design based only on a thermal ratchet.

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“…This and other relevant recent results [14][15][16][17][18][19][20][21][22][23] have been applied to compute the efficiency of other feedback systems [13,21,[24][25][26]. This recent burst of theoretical works on the thermodynamics of feedback systems has been accompanied by experimental realizations [27][28][29], and they have made it possible to start to solve several of the open questions in the field [30,31]. These developments are built over the proposal of the Maxwell demon [32], the important early contributions done by Szilard, Landauer, and Bennett, among others [33][34][35], and the concepts and formalism provided by the theory of information [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Efficiency at maximum power of a discrete feedback ratchet

2016

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Efficiency at maximum power is found to be of the same order for a feedback ratchet and for its open-loop counterpart. However, feedback increases the output power up to a factor of five. This increase in output power is due to the increase in energy input and the effective entropy reduction obtained as a consequence of feedback. Optimal efficiency at maximum power is reached for time intervals between feedback actions two orders of magnitude smaller than the characteristic time of diffusion over a ratchet period length. The efficiency is computed consistently taking into account the correlation between the control actions. We consider a feedback control protocol for a discrete feedback flashing ratchet, which works against an external load. We maximize the power output optimizing the parameters of the ratchet, the controller, and the external load. The maximum power output is found to be upper bounded, so the attainable extracted power is limited. After, we compute an upper bound for the efficiency of this isothermal feedback ratchet at maximum power output. We make this computation applying recent developments of the thermodynamics of feedback-controlled systems, which give an equation to compute the entropy reduction due to information. However, this equation requires the computation of the probability of each of the possible sequences of the controller's actions. This computation becomes involved when the sequence of the controller's actions is non-Markovian, as is the case in most feedback ratchets. We here introduce an alternative procedure to set strong bounds to the entropy reduction in order to compute its value. In this procedure the bounds are evaluated in a quasi-Markovian limit, which emerge when there are big differences between the stationary probabilities of the system states. These big differences are an effect of the potential strength, which minimizes the departures from the Markovianicity of the sequence of control actions, allowing also to minimize the departures from the optimal performance of the system. This procedure can be applied to other feedback ratchets and, more in general, to other control systems.

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Open Problems on Information and Feedback Controlled Systems

Cited by 14 publications

References 57 publications

Delay-induced transport in a rocking ratchet under feedback control

Delay-induced transport in a rocking ratchet under feedback control

Motor properties from persistence: a linear molecular walker lacking spatial and temporal asymmetry

Efficiency at maximum power of a discrete feedback ratchet

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