Information and flux in a feedback controlled Brownian ratchet

Cao, Francisco J.; Feito, M.; Touchette, Hugo

doi:10.1016/j.physa.2008.10.006

Cited by 43 publications

(65 citation statements)

References 25 publications

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“…Still, there is no complete theoretical framework detailing the relationship between feedback and thermodynamics. Interest in developing such a framework -a thermodynamics of feedback -has grown recently in part due to experiments on feedback cooling [3,4] and feedback control of nanoparticles [5,6]; experimental, computational, and theoretical studies of feedback driven Brownian ratchets [7][8][9][10][11][12]; and new theoretical predictions relating dissipation to information [13][14][15][16][17][18][19][20][21][22][23].Recently, Sagawa and Ueda derived a generalization of the second law of thermodynamics for quantum and classical systems manipulated by one feedback loop [18,19], which subsequently has been verified experimentally [24] and extended to classical systems driven by repeated discrete feedback -implemented through a series of feedback loops initiated at predetermined times -independently by Horowitz and Vaikuntanathan [20], and Fujitani and Suzuki [21]. The second law of thermodynamics for discrete feedback states that the average work dissipated W d in driving a system with a discrete feedback protocol from one equilibrium state at inverse temperature β to another at the same temperature is related to the microscopic information gained through measurements I by…”

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confidence: 99%

Thermodynamic reversibility in feedback processes

Horowitz

Parrondo

2011

EPL

117

160

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Abstract. -The sum of the average work dissipated plus the information gained during a thermodynamic process with discrete feedback must exceed zero. We demonstrate that the minimum value of zero is attained only by feedback-reversible processes that are indistinguishable from their time-reversal, thereby extending the notion of thermodynamic reversibility to feedback processes. In addition, we prove that in every realization of a feedback-reversible process the sum of the work dissipated and change in uncertainty is zero.Investigations into the thermodynamic implications of feedback have a long history [1,2], especially with regard to the relationship between information acquisition and thermodynamic quantities -such as work, heat, and entropy. Still, there is no complete theoretical framework detailing the relationship between feedback and thermodynamics. Interest in developing such a framework -a thermodynamics of feedback -has grown recently in part due to experiments on feedback cooling [3,4] and feedback control of nanoparticles [5,6]; experimental, computational, and theoretical studies of feedback driven Brownian ratchets [7][8][9][10][11][12]; and new theoretical predictions relating dissipation to information [13][14][15][16][17][18][19][20][21][22][23].Recently, Sagawa and Ueda derived a generalization of the second law of thermodynamics for quantum and classical systems manipulated by one feedback loop [18,19], which subsequently has been verified experimentally [24] and extended to classical systems driven by repeated discrete feedback -implemented through a series of feedback loops initiated at predetermined times -independently by Horowitz and Vaikuntanathan [20], and Fujitani and Suzuki [21]. The second law of thermodynamics for discrete feedback states that the average work dissipated W d in driving a system with a discrete feedback protocol from one equilibrium state at inverse temperature β to another at the same temperature is related to the microscopic information gained through measurements I byHere, I is the mutual information between the state of the system and the measurement outcome [18,19,25], and the average work dissipated is the average work W done in excess of the average free-energy difference ∆F : The second law of the thermodynamics plays a central role within the framework of thermodynamics. Besides restricting the realizability of thermodynamic processes, it distinguishes particular processes that produce no entropy. In macroscopic systems, such processes are called reversible, because the sequence of equilibrium states visited by the system during the process can be traversed both forwards and backwards [26]. At the microscopic level the connection between entropy production and reversibility must be interpreted statistically and is quantified mathematically by the distingiushibility of a thermodynamic process from its time-reversal [22,23,27]. Like the second law of thermodynamics, eq. (1) singles out particular processes that have no dissipation [β W d + I = 0]. Because suc...

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mentioning

confidence: 99%

Thermodynamic reversibility in feedback processes

Horowitz

Parrondo

2011

EPL

117

160

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“…For big enough potential heights, V 0 k B T , the stopping force is F stop 3 4 V 0 , whereas for small potential heights, V 0 k B T , it is F stop 1 4 V 0 . In both limiting cases, the stopping force is proportional to V 0 , as found in the continuous case [11,12]. We can also look for the force F * that maximizes the mean power P = J (1) s F at fixed V 0 .…”

Section: Dynamics: Flux Of Particlesmentioning

confidence: 90%

“…In addition, flux and power performance have been studied as a function of the amount of information used by the controller [11,12]. In this paper, we address the computation of the efficiency of a feedback flashing ratchet as an application of the recent results on the thermodynamics of feedback-controlled systems presented in Ref.…”

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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“…However, for these later systems no systematic study on the role of information has been performed. On the other hand, for feedback flashing ratchets, relations between the information I (about the system) gathered by the controller per step and the performance have been recently obtained [38,39]. These relations have been established for a collective feedback flashing ratchet compounded of one or few particles, considering the optimal protocol for one particle and its generalization to few particles.…”

Section: Feedback Controlled Ratchets and Informationmentioning

confidence: 99%

“…The computations in [38] have shown that the maximum increase in the flux that can be obtained has an upper bound proportional to the square root of the information I received in each step, i.e.,…”

Section: Feedback Controlled Ratchets and Informationmentioning

confidence: 99%

Open Problems on Information and Feedback Controlled Systems

Cao

Feito

2012

Entropy

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Feedback or closed-loop control allows dynamical systems to increase their performance up to a limit imposed by the second law of thermodynamics. It is expected that within this limit, the system performance increases as the controller uses more information about the system. However, despite the relevant progresses made recently, a general and complete formal development to justify this statement using information theory is still lacking. We present here the state-of-the-art and the main open problems that include aspects of the redundancy of correlated operations of feedback control and the continuous operation of feedback control. Complete answers to these questions are required to firmly establish the thermodynamics of feedback controlled systems. Other relevant open questions concern the implications of the theoretical results for the limitations in the performance of feedback controlled flashing ratchets, and for the operation and performance of nanotechnology devices and biological systems.

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Information and flux in a feedback controlled Brownian ratchet

Cited by 43 publications

References 25 publications

Thermodynamic reversibility in feedback processes

Thermodynamic reversibility in feedback processes

Efficiency at maximum power of a discrete feedback ratchet

Open Problems on Information and Feedback Controlled Systems

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