Merits and qualms of work fluctuations in classical fluctuation theorems

Deng, Jiawen; Tan, Alvis Mazon; Hänggi, Peter; Gong, Jiangbin

doi:10.1103/physreve.95.012106

Cited by 13 publications

(16 citation statements)

References 52 publications

(63 reference statements)

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“…Somewhat surprisingly, we recently found the possibility of obtaining a systematic divergence in var e −βW in classical systems, as verified computationally in simple models isolated from a bath [26]. This divergence has immediate implications for the applicability of JE in measuring ∆F, but was seldom mentioned previously except in some general discussions made in Ref.…”

Section: Introductionmentioning

confidence: 65%

“…where Ω 0 and Ω τ act like the initial and final "energy index" while P(Ω τ |Ω 0 ) is the transition probability between the states under a certain protocol, which is defined in [26] and is proven to be bi-stochastic. Note here that the lower bounds Ω 0 , Ω τ = 0 correspond to minimum of the lower bounded energy under fixed λ 0 , λ τ .…”

Section: A General Discussionmentioning

confidence: 99%

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Deformed Jarzynski Equality

Deng

Jaramillo

Hänggi

et al. 2017

Entropy

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Abstract:The well-known Jarzynski equality, often written in the form e −β∆F = e −βW , provides a non-equilibrium means to measure the free energy difference ∆F of a system at the same inverse temperature β based on an ensemble average of non-equilibrium work W. The accuracy of Jarzynski's measurement scheme was known to be determined by the variance of exponential work, denoted as var e −βW . However, it was recently found that var e −βW can systematically diverge in both classical and quantum cases. Such divergence will necessarily pose a challenge in the applications of Jarzynski equality because it may dramatically reduce the efficiency in determining ∆F. In this work, we present a deformed Jarzynski equality for both classical and quantum non-equilibrium statistics, in efforts to reuse experimental data that already suffers from a diverging var e −βW . The main feature of our deformed Jarzynski equality is that it connects free energies at different temperatures and it may still work efficiently subject to a diverging var e −βW . The conditions for applying our deformed Jarzynski equality may be met in experimental and computational situations. If so, then there is no need to redesign experimental or simulation methods. Furthermore, using the deformed Jarzynski equality, we exemplify the distinct behaviors of classical and quantum work fluctuations for the case of a time-dependent driven harmonic oscillator dynamics and provide insights into the essential performance differences between classical and quantum Jarzynski equalities.

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Section: Introductionmentioning

confidence: 65%

Section: A General Discussionmentioning

confidence: 99%

Deformed Jarzynski Equality

Deng

Jaramillo

Hänggi

et al. 2017

Entropy

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“…Indeed, in contrast to JE itself which is always well behaved, var(e −βW dis ) can diverge, suggesting higher-energy components from the initial Gibbs distribution may contribute even more to the variance. Surprisingly, prior to our work [29], this possibility of divergence was rarely mentioned, with one exception [23] treating an adiabatic work protocol. According to the principle of minimal work fluctuations (PMWF) [29,30], once var(e −βW dis ) diverges for an adiabatic protocol, then it will suffer from analogous divergence under arbitrary work protocols sharing the same initial and final system Hamiltonians.…”

mentioning

confidence: 99%

“…Surprisingly, prior to our work [29], this possibility of divergence was rarely mentioned, with one exception [23] treating an adiabatic work protocol. According to the principle of minimal work fluctuations (PMWF) [29,30], once var(e −βW dis ) diverges for an adiabatic protocol, then it will suffer from analogous divergence under arbitrary work protocols sharing the same initial and final system Hamiltonians. The accuracy in estimating ∆F in such situations becomes problematic.…”

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confidence: 99%

Quantum work fluctuations in connection with the Jarzynski equality

2017

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A result of great theoretical and experimental interest, the Jarzynski equality predicts a free energy change ΔF of a system at inverse temperature β from an ensemble average of nonequilibrium exponential work, i.e., 〈e^{-βW}〉=e^{-βΔF}. The number of experimental work values needed to reach a given accuracy of ΔF is determined by the variance of e^{-βW}, denoted var(e^{-βW}). We discover in this work that var(e^{-βW}) in both harmonic and anharmonic Hamiltonian systems can systematically diverge in nonadiabatic work protocols, even when the adiabatic protocols do not suffer from such divergence. This divergence may be regarded as a type of dynamically induced phase transition in work fluctuations. For a quantum harmonic oscillator with time-dependent trapping frequency as a working example, any nonadiabatic work protocol is found to yield a diverging var(e^{-βW}) at sufficiently low temperatures, markedly different from the classical behavior. The divergence of var(e^{-βW}) indicates the too-far-from-equilibrium nature of a nonadiabatic work protocol and makes it compulsory to apply designed control fields to suppress the quantum work fluctuations in order to test the Jarzynski equality.

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“…This classical TPM scheme could in principle be implemented and it would verify the JE, but it would hardly be considered as a breakthrough for the experimental accessibility of equilibrium quantities through nonequilibrium processes. We emphasize that this is not an insufficiency of the possible experimental realizations, such as finite number of runs, noise, energy stored in the control system, or problems with convergence [6,[56][57][58][59][60]] but a conceptual issue of the TPM scheme.…”

Section: On the Practical Relevance Of Tpm-jesmentioning

confidence: 99%

Work as an external quantum observable and an operational quantum work fluctuation theorem

Beyer

Luoma

Strunz

2020

Phys. Rev. Research

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We propose a definition of externally measurable quantum work in driven systems. Work is given as a quantum observable on a control device which is forcing the system and can be determined without knowledge of the system HamiltonianĤ S. We argue that quantum work fluctuation theorems which rely on the knowledge of H S are of little practical relevance, contrary to their classical counterparts. Using our framework, we derive a fluctuation theorem which is operationally accessible and could in principle be implemented in experiments to determine bounds on free energy differences of unknown systems.

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Merits and qualms of work fluctuations in classical fluctuation theorems

Cited by 13 publications

References 52 publications

Deformed Jarzynski Equality

Deformed Jarzynski Equality

Quantum work fluctuations in connection with the Jarzynski equality

Work as an external quantum observable and an operational quantum work fluctuation theorem

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