Nonequilibrium work equalities in isolated quantum systems

Liu, Fei; Ouyang, Zhen

doi:10.1088/1674-1056/23/7/070512

Cited by 8 publications

(14 citation statements)

References 122 publications

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“…Although this new form does not bring any advantages in computing over the original ones, Eqs. (29) and (34), it indeed corresponds to the celebrated Feynman-Kac formula in classical stochastic processes [10,11,15,16,94,110]. Analogously, the concise expressions of the CFs of the heat and entropy production are given by…”

Section: Appendix A: Multitime Correlation Function Of Operatorsmentioning

confidence: 84%

Characteristic functions based on a quantum jump trajectory

Liu

2016

Phys. Rev. E

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Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A conventional procedure for obtaining these functions is to resort to a first-principles approach; namely, the evolution equations of the CFs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system. However, the QMEs can be unraveled by a quantum jump trajectory. Thermodynamic quantities such as the heat, work, and entropy production can be well defined along a trajectory. Hence, on the basis of the notion of a trajectory, can we straightforwardly derive these CFs, e.g., their evolution equations? This is essential to establish the self-contained stochastic thermodynamics of a QME. In this paper, we show that it is indeed plausible and also simple. Particularly, these equations are fully consistent with those obtained by the first-principles method. Our results have practical significance; they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments.

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Section: Appendix A: Multitime Correlation Function Of Operatorsmentioning

confidence: 84%

Characteristic functions based on a quantum jump trajectory

Liu

2016

Phys. Rev. E

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“…This condition plays a key role in the validity of the work equalities [23,34] and in the following discussions. Master equation (1) is widely utilized in quantum optics, e.g., in describing resonance fluorescence [35].…”

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confidence: 97%

“…In order to formulate a quantum JE, in a closed quantum system, a two-energy measurements (TEM) scheme was proposed by Kurchan [2] to define the work. Although this definition still faces criticisms related to the fact that the scheme may destroy the initial quantum-coherent superposition of the system [33], it has been widely accepted in the field [12,13,34]. Because closed quantum systems are not common in reality, there have also been many attempts to generalize this definition to include open quantum systems [35].…”

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confidence: 99%

“…First, I explicitly write its whole Hamiltonian, H(t ′ )=H 0 +H 1 (t ′ )+H r +V . There exists the following evolution equation relating to the operator, K(t ′ ; µ) [34]: …”

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confidence: 99%

“…On the other hand, when one carries out formal derivations, in some cases the forward method is more convenient than the backward method, or vice versa. For instance, one can easily obtain a concise expression related to the work equality if the backward method is used [23,24,34].…”

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confidence: 99%

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Calculating work in weakly driven quantum master equations: Backward and forward equations

Liu

2016

Phys. Rev. E

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I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on two energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed. Introduction. Recently, there has been growing interest in the heat and work of nonequilibrium quantum processes . Studies focusing on this issue have mainly been motivated by an interest in extending the important classical fluctuation relations into the quantum regime, e.g., the celebrated Bochkov-Kuzovlev equality [1] and the Jarzynski equality (JE) [31].Compared with their classical counterparts [32], which are physically intuitive, the definitions of fluctuating heat and work become very delicate in the quantum case. In order to formulate a quantum JE, in a closed quantum system, a two-energy measurements (TEM) scheme was proposed by Kurchan [2] to define the work. Although this definition still faces criticisms related to the fact that the scheme may destroy the initial quantum-coherent superposition of the system [33], it has been widely accepted in the field [12,13,34]. Because closed quantum systems are not common in reality, there have also been many attempts to generalize this definition to include open quantum systems [35]. These efforts can be roughly divided into two types of method. The first type [11,12,25] involves the combination of the system and its surrounding heat reservoir as a composite system. The TEM scheme is then conducted on the system and reservoir. As the interaction between these is weak, the energy eigenvalue change obtained using the TEM for the system is referred to as the internal energy change, while the energy eigenvalue change obtained by the TEM for the reservoir is referred to as the heat released from the system, Q T EM . Therefore, the work done on the open system, W T EM , is the sum of the internal energy change and the heat. The second type of method is based on the quantum jump trajectory (QJT) that is unraveled from the Lindblad quantum master equations [6,9,17,18,[21][22][23][24]36]. Under this notion, the energy change of the heat reservoir is continuously measured. This is interpreted as the released heat along a trajectory, Q QJT . If one preserves the internal energy change of the system mentioned above, an alternative work, W QJT , is then the sum of the heat and internal energy change along the same trajectory. Figure (1) schematically illustrates the difference between these two types of work in a two-level qu...

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Statistics of work done in a degenerate parametric amplification process

Yadalam

Harbola

2019

Phys. Rev. A

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Nonequilibrium work equalities in isolated quantum systems

Cited by 8 publications

References 122 publications

Characteristic functions based on a quantum jump trajectory

Characteristic functions based on a quantum jump trajectory

Calculating work in weakly driven quantum master equations: Backward and forward equations

Statistics of work done in a degenerate parametric amplification process

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