Thermodynamics of feedback controlled systems

Cao, Francisco J.; Feito, M.

doi:10.1103/physreve.79.041118

Cited by 137 publications

(165 citation statements)

References 27 publications

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“…It would be interesting, however, to model this mechanism explicitly within a Hamiltonian framework, either by introducing additional degrees of freedom to model the demon or by specifying coupling terms between the measurement device and the system. In this case, we anticipate that the bound on extracted work will be given in terms of the correlation between the state of the system and the state of the measuring device and/or demon [28,29,31,33].…”

Section: Discussionmentioning

confidence: 99%

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Modeling Maxwell’s demon with a microcanonical Szilard engine

Vaikuntanathan

Jarzynski

2011

Phys. Rev. E

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Following recent work by Marathe and Parrondo [PRL, 104, 245704 (2010)], we construct a classical Hamiltonian system whose energy is reduced during the adiabatic cycling of external parameters, when initial conditions are sampled microcanonically. Combining our system with a device that measures its energy, we propose a cyclic procedure during which energy is extracted from a heat bath and converted to work, in apparent violation of the second law of thermodynamics. This paradox is resolved by deriving an explicit relationship between the average work delivered during one cycle of operation, and the average information gained when measuring the system's energy.

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Section: Discussionmentioning

confidence: 99%

“…Dropping the subscript 0, we now introduce two probability distributions (compare with Eqs. 32,33) f X (z) ≡ P (z|X) = P (z, X)/P X (A3)…”

Section: Appendix A: Analysis Of Error-prone Measurement Devicesmentioning

confidence: 99%

Modeling Maxwell’s demon with a microcanonical Szilard engine

Vaikuntanathan

Jarzynski

2011

Phys. Rev. E

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“…This energy cost, known as Landauer's erasure cost because it is incurred when information is erased, effectively prevents Maxwell's demon-type engines, like feedback ratchets, to have efficiencies greater than one (as required by the second law of thermodynamics) [13]. The calculation of this energy cost requires the computation of the mutual information between the controlled system and the controller, conditioned on the past history of the controller's evolution [15,21]. The role of the conditioning is to take into account the correlations between the measurements, and to avoid redundancies in the computation of the entropy reduction.…”

Section: Discussionmentioning

confidence: 99%

Information and flux in a feedback controlled Brownian ratchet

Cao

Feito

Touchette

2009

Physica A: Statistical Mechanics and its Applications

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We study a feedback control version of the flashing Brownian ratchet, in which the application of the flashing potential depends on the state of the particles to be controlled. Taking the view that the ratchet acts as a Maxwell's demon, we study the relationship that exists between the performance of the demon as a rectifier of random motion and the amount of information gathered by the demon through measurements. In the context of a simple measurement model, we derive analytic expressions for the flux induced by the feedback ratchet when acting on one particle and a few particles, and compare these results with those obtained with its open-loop version, which operates without information. Our main finding is that the flux in the feedback case has an upper bound proportional to the square-root of the information. Our results provide a quantitative analysis of the value of information in feedback ratchets, as well as an effective description of imperfect or noisy feedback ratchets that are relevant for experimental applications.

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“…Recently, Crooks type studies have also been attempted in these kind of systems [11][12][13]. In all these studies the possibility of entropy production due to the interaction between the system and the measurement apparatus was not well considered except the study by Cao and Feito [14] in which, they have given a way to compute the entropy reduction in feedback controlled system due to repeated operation of controller. It is quite natural to ask, what would be the total amount of entropy production Σ of the "full" system (the system + reservoir + feedback controller) ?…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control

Kundu

2012

Phys. Rev. E

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Without violating causality, we allow performing measurements in time reverse process of a feedback manipulated stochastic system. As a result we come across an entropy production due to the measurement process. This entropy production, in addition to the usual system and medium entropy production, constitutes the total entropy production of the combined system of the reservoir, the system and the feedback controller. We show that this total entropy production of "full" system satisfies an integrated fluctuation theorem as well as a detailed fluctuation theorem as expected. We illustrate and verify this idea through explicit calculation and direct simulation in two examples.

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Thermodynamics of feedback controlled systems

Cited by 137 publications

References 27 publications

Modeling Maxwell’s demon with a microcanonical Szilard engine

Modeling Maxwell’s demon with a microcanonical Szilard engine

Information and flux in a feedback controlled Brownian ratchet

Nonequilibrium fluctuation theorem for systems under discrete and continuous feedback control

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