Exact fluctuation theorem without ensemble quantities

Cuetara, Gregory Bulnes; Esposito, Massimiliano; Imparato, Alberto

doi:10.1103/physreve.89.052119

Cited by 38 publications

(48 citation statements)

References 35 publications

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“…It is important to stress that the choice of borders and appropriate associated thermodynamic quantities is the key to obtaining exact transient fluctuation relations, such as in equation (5), that is, fluctuation relations that hold regardless of the time duration of the process under investigation [2,18,52,53]. In the long time limit, steady-state fluctuation relations hold which are independent of the border choice.…”

Section: The Heat Engine Fluctuation Relation (Hefr)mentioning

confidence: 99%

Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

2015

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We study stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency greater than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) are illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid-state implementations with Cooper-pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events. -10], this is typically impossible in a quantum system. In the quantum scenario, the situation is greatly complicated by the invasiveness of the measurement apparatus, which can lead to collapse of the wave function. The prescription accordingly is to measure the energy of the system twice (at the beginning and end of the forcing protocol) by means of two projective measurements and obtain the work as their difference [11][12][13][14].This two-measurement scheme has, however, proved challenging from an experimental point of view [15,16], so much so that it has been carried out only very recently [17]. This occurrence has triggered the OPEN ACCESS RECEIVED 1 2 , i.e., the first subsystem is assumed to be not colder than the second at the initial time. Also we assume that at all times the Hamiltonian is time reversal symmetric [48]. We further assume that the compound system is thermally isolated and that the driving is New J. Phys. 17 (2015) 035012 M Campisi et al

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Section: The Heat Engine Fluctuation Relation (Hefr)mentioning

confidence: 99%

Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

2015

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“…Quite remarkably, this is true despite the quantum coherences in the Floquet basis introduced by the initial measurement of the system energy. We further consider the long time limit and formally establish a steady-state FT for the currents and mechanical power [10].…”

Section: Stochastic Thermodynamicsmentioning

confidence: 99%

“…Up to now, a consistent picture of the thermodynamics of these systems has only been given within specific limits or regimes. In particular, most studies have been focused on slowly driven and weakly coupled open systems [6][7][8][9][10]. Within this regime, the system dynamics is well described by a stochastic master equation in the basis of time dependent energies of the system.…”

Section: Introductionmentioning

confidence: 99%

“…We make use of the LDB condition in order to write the steady-state entropy production in terms of the currents and mechanical power. A steady-state FT for these quantities is also established by using the LDB, which is the steady-state version of the transient FT obtained in [10]. A steady-state FT for the mechanical power is recovered when considering a single heat reservoir [17,19].…”

Section: Introductionmentioning

confidence: 99%

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Stochastic thermodynamics of rapidly driven systems

2015

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We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the Floquet basis. Transition rates are shown to satisfy the local detailed balance involving the entropy flowing out of the reservoirs. The first and second law of thermodynamics are also identified at the trajectory level. Mechanical work is identified by means of initial and final projections on energy eigenstates of the system. We explicitly show that this two step measurement becomes unnecessary in the long time limit. A steady-state fluctuation theorem for the currents and rate of mechanical work is also established. This relation does not require the introduction of a time reversed external driving which is usually needed when considering systems subjected to time asymmetric external fields. This is understood as a consequence of the secular approximation applied in consistency with the large time scale separation between the fast driving oscillations and the slower relaxation dynamics induced by the environment. Our results are finally illustrated on a model describing a thermodynamic engine.

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“…Finally, we mention a particular scenario for the total EP described in [37] which reproduces the echo state. A system in contact with several reservoirs is prepared so that its initial state is the equilibrium distribution of one particular reservoir at λ 0 .…”

Section: Processes Starting From the Echo Statementioning

confidence: 99%

Echo states for detailed fluctuation theorems

et al. 2015

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Detailed fluctuation theorems are statements about the probability distribution for the stochastic entropy production along a trajectory. It involves the consideration of a suitably transformed dynamics, such as the time reversed, the adjoint, or a combination of these. We identify specific, typically unique, initial conditions, called echo states, for which the final probability distribution of the transformed dynamics reproduces the initial distribution. In this case the detailed fluctuation theorems relate the stochastic entropy production of the direct process to that of the transformed one. We illustrate our results by an explicit analytical calculation and numerical simulations for a modulated two-state quantum dot.

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Exact fluctuation theorem without ensemble quantities

Cited by 38 publications

References 35 publications

Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments

Stochastic thermodynamics of rapidly driven systems

Echo states for detailed fluctuation theorems

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