Optimal driving of isothermal processes close to equilibrium

Bonança, Marcus V. S.; Deffner, Sebastian

doi:10.1063/1.4885277

Cited by 91 publications

(151 citation statements)

References 45 publications

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“…Our experimental system is a parallel RC circuit driven by an alternating current. We verify the fluctuation theorem (1) for processes of arbitrary durations for different driving frequencies and intensities, where we go far beyond the slow driving considered in [30,31]. Furthermore, we show the difference between conjugated entropy production and entropy produced in the backward process.…”

Section: Introductionsupporting

confidence: 69%

“…Hence, we assume that the time reverse process starts just after the forward process ends, at time t t 1 = . The control parameter is then varied according to t t t t ( ) ( ) 6 In fact, in the setup of [31], the macroscopic state is time periodic and the succession of forward and backward processes correspond to one period. The experiments described in [3,23,25,33] involve transitions between (equilibrium or non-equilibrium) stationary states.…”

Section: Detailed Fluctuation Theorem For the Transition Between Two mentioning

confidence: 99%

“…This fluctuation theorem has been experimentally tested for the transition between equilibrium states [3,33], where it reduces to Crooks' relation [7], for non-equilibrium steady-states [25,27], and in the transition between nonequilibrium steady-states [23], where it can be refined to give the Hatano-Sasa relation [9]. More recently, the fluctuation theorem (1) was observed in a more general experiment involving a periodically driven system in contact with two heat baths at different temperatures [31]. All the aforementioned experiments have this in common, that at the end of the backward process, the system is in the same macroscopic state as at the beginning of the forward process 6 .…”

Section: Introductionmentioning

confidence: 99%

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Fluctuation theorem between non-equilibrium states in anRCcircuit

et al. 2015

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Fluctuation theorems impose constraints on the probability of observing negative entropy production in small systems driven out of equilibrium. The range of validity of fluctuation theorems has been extensively tested for transitions between equilibrium and non-equilibrium stationary states, but not between general non-equilibrium states. Here we report an experimental verification of the detailed fluctuation theorem for the total amount of entropy produced in the isothermal transition between two non-equilibrium states. The experimental setup is a parallel RC circuit driven by an alternating current. We investigate the statistics of the heat released, of the variation of the entropy of the system, and of the entropy produced for processes of different durations. We show that the fluctuation theorem is satisfied with high accuracy for current drivings at different frequencies and different amplitudes. OPEN ACCESS RECEIVED

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Section: Introductionsupporting

confidence: 69%

Section: Detailed Fluctuation Theorem For the Transition Between Two mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fluctuation theorem between non-equilibrium states in anRCcircuit

et al. 2015

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“…This result was further precised [27] and recently a similar argumentation was successfully used for general thermodynamic devices [28]. Further universalities were obtained for the class of heat engines working in the regime of "low dissipation" [15,[29][30][31][32][33], where the work dissipated during the * viktor.holubec@mff.cuni.cz isothermal branches of the Carnot cycle grows in inverse proportion to the duration of these branches. Namely a general expression for the EMP for these engines has been published [15] and subsequently lower and upper bounds on the EMP were derived [29].…”

Section: Introductionmentioning

confidence: 84%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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“…Universal features and bounds for the efficiency at maximum power of finite-time Carnot cycles were identified in [18,[27][28][29] for generic heat engines. Other results were obtained combining MMEs and linear response theory [7,30,31] and similar approaches were used to demonstrate the universality of heat engines in the limit of infinitesimal cycles [32]. Outside the field of thermodynamics, our theory of slowly driven open quantum systems also contributes to the current research activity on quantum adiabatic driving.…”

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 98%

Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

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We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasi-static transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated to an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.A central result in the study of open quantum systems [1, 2] is the Markovian Master Equation (MME) approach which, under realistic assumptions, describes the temporal evolution of a system of interest A induced by a weak coupling with a large external environment E. This consists in a first order linear differential equatioṅ ρ(t) = L[ρ(t)] where ρ(t) is the density matrix of A and where the generator of the dynamics is provided by a quantum Liouvillian superoperator L that can be casted in the so called Gorini-Kossakowski-Sudarshan-Lindblad form [3][4][5]. For autonomous systems the latter does not exhibit an explicit time dependence and the dynamics of A exponentially relaxes to a (typically unique) equilibrium steady state ρ 0 identified by the null eigenvector equation L[ρ 0 ] = 0. MMEs can also be employed to describe the temporal evolution of A when it is tampered by the presence of slow varying, external driving forces. Indeed, as long as these operate on a time scale which is much larger than the characteristic bath correlations times and the inverse frequencies of the system of interest, the effective coupling between A and E adapts instantaneously to the driving control, resulting on a MME governed by a time-dependent Liouvillian generator, i.e.An explicit integration of this equation is in general difficult to obtain. Yet, if the control forces are so slow that their associated time scale is also larger with respect to the relaxation time of the system induced by the interaction with E, one expects ρ(t) to approximately follow the instantaneous equilibrium state ρ 0 (t) that nullifies L t . Our aim is to estimate quantitative deviations from this ultra-slow driving regime. For this purpose we develop a perturbation theory valid in the limit of slowly varying Liouvillians L t and derive a formal solution of Eq. (1) which allows one to evaluate non-equilibrium corrections up to arbitrary order. The main motivation of our analysis is to model thermodynamic processes and cycles beyond the usual reversible limit which is strictly valid only for infinitely long quasi-static transformations. Finite-time thermodynamics [7,8]...

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Optimal driving of isothermal processes close to equilibrium

Cited by 91 publications

References 45 publications

Fluctuation theorem between non-equilibrium states in anRCcircuit

Fluctuation theorem between non-equilibrium states in anRCcircuit

Efficiency at and near maximum power of low-dissipation heat engines

Slow Dynamics and Thermodynamics of Open Quantum Systems

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