Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method

Liu, Fei

doi:10.1103/physreve.90.032121

Cited by 29 publications

(24 citation statements)

References 62 publications

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“…whose positivity follows from (18). This provides an alternative thermodynamic proof of the well-known property that unital maps can only increase the von Neumann entropy [2].…”

Section: B Unital Work Relationsmentioning

confidence: 95%

“…General quantum Markov semigroups were explored by Crooks using time-reversed or dual maps [14], which were then applied by Horowitz et al to nonequilibrium quantum jump trajectories [5,15]. An alternative, operator formulation for driven Lindbald master equations was independently developed by Chetrite and Mallick [16], and its equivalence to the quantum jump approach was investigated by Liu [17,18]. Fluctuation theorems under unital CPTP maps for thermodynamic quantities, like work, energy, and information-theoretic entropy, have appeared in numerous works [19][20][21], while predictions for nonunital CPTP maps usually take the form of an integral fluctuation theorem with a so-called correction [6,[20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium potential and fluctuation theorems for quantum maps

2015

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We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem reproduces well-known fluctuation theorems in a single and simplified framework and extends the Hatano-Sasa theorem to quantum nonequilibrium processes. Moreover, it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system.

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“…whose positivity follows from (18). This provides an alternative thermodynamic proof of the well-known property that unital maps can only increase the von Neumann entropy [2].…”

Section: B Unital Work Relationsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Nonequilibrium potential and fluctuation theorems for quantum maps

2015

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show abstract

“…More recently, work has been done on the study of thermodynamic properties of open quantum systems driven by a fast and periodic external field, whether weakly coupled to a single heat reservoirs [4,[14][15][16][17][18][19] or arranged in a specific implementation of a heat engine [20,21]. In the present paper, we perform the general ST analysis of an open quantum system weakly coupled to multiple heat or chemical reservoirs, and driven by a fast and time periodic external force.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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“…The effect of time-dependent dissipation on work has been previously studied theoretically in the adiabatic limit [7,48]. However, these studies do not provide quantitative estimates on the correction induced by the finite speed of driving on the work distributions.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations of work in nearly adiabatically driven open quantum systems

et al. 2015

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We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving, such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

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Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method

Cited by 29 publications

References 62 publications

Nonequilibrium potential and fluctuation theorems for quantum maps

Nonequilibrium potential and fluctuation theorems for quantum maps

Stochastic thermodynamics of rapidly driven systems

Fluctuations of work in nearly adiabatically driven open quantum systems

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