Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence

Tajima, Hiroyasu; Funo, Ken

doi:10.48550/arxiv.2004.13412

Cited by 4 publications

(8 citation statements)

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“…Appendix A: Derivation of (18) We derive (18). By variable transformation s = γ(t − u), (17) becomes…”

Section: Appendix D: Calculation Of Entropy Productionmentioning

confidence: 99%

“…Time-dependent open systems have been studied actively in recent years. These studies relate to quantum pump [1][2][3][4][5][6][7][8], excess entropy production [9][10][11][12][13], efficiency and power of heat engine [14][15][16][17][18], shortcuts to adiabaticity [19,20], and speed limits [21][22][23]. In the studies of quantum pumping and excess entropy production for systems governed by the master equation, the time dependence is described using the pseudo-inverse of the Liouvillian [1-3, 5-7, 12, 13, 24].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic expansion of the solution of the master equation and its application to the speed limit

Nakajima,

Utsumi

2021

Preprint

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We investigate an asymptotic expansion of the solution of the master equation under the modulation of control parameters. In this case, the dominant part of the solution becomes the dynamical steady state expressed as an infinite series using the pseudo-inverse of the Liouvillian, whose convergence is not granted in general. We demonstrate that for the relaxation time approximation, the Borel summation of the infinite series is compatible with the exact solution. By exploiting the series expansion, we obtain the analytic expression of the heat. In the two-level system coupled to a single bath, we consider that the linear modulation of the energy as a function of time and demonstrate that the infinite series expression is the asymptotic expansion of the exact solution. The equality of a trade-off relation between the speed of the state transformation and the entropy production (Shiraishi, Funo, and Saito, Phys. Rev. Lett. 121, 070601 (2018)) holds in the lowest order of the frequency of the energy modulation in the two-level system. To obtain this result, the heat emission and absorption at edges (the initial and end times) or the differences of the Shannon entropy between the instantaneous steady state and the dynamical steady state at edges are essential: If we ignore these effects, the trade-off relation can be violated.

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“…Appendix A: Derivation of (18) We derive (18). By variable transformation s = γ(t − u), (17) becomes…”

Section: Appendix D: Calculation Of Entropy Productionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic expansion of the solution of the master equation and its application to the speed limit

Nakajima,

Utsumi

2021

Preprint

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“…In this paper, we focus on thermodynamic processes that involve Markovian open quantum systems described in terms of Lindblad master equations [29,30]. Even though several previous works have investigated generalized thermodynamic uncertainty relations in this setting [31][32][33][34][35][36][37][38][39], the behavior of the uncertainty product (1) has not yet been systematically explored. Our goal is thus to determine whether a trade-off between fluctuations and dissipation still holds for these systems and, if so, how much it can be alleviated by quantum effects compared to the original uncertainty relation.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic uncertainty relations for coherently driven open quantum systems

Menczel,

Loisa,

Brandner

et al. 2021

Preprint

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In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian open quantum systems. We first consider three instructive examples and then systematically minimize the product of uncertainty and entropy production for small open quantum systems. As our main result, we find that the thermodynamic cost of reducing fluctuations can be lowered below the classical bound by coherence. We conjecture that this cost can be made arbitrarily small in quantum systems with sufficiently many degrees of freedom. Our results thereby provide a general guideline for the design of thermal machines in the quantum regime that operate with high thermodynamic precision, meaning low dissipation and small fluctuations around average values.

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“…Theoretically, an open quantum system is considered as the working medium [20], and relevant quantities such as work, heat and efficiency are characterized by analogy of the classical heat engines [21]. Especially, for a finite-time heat engine, there is a trade-off relation between power and efficiency [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [23], by using an abstract system called a 2N -state model (that is not directly related to a qubit system), they show that quantum coherence among degenerate states can enhance a scaling of the power. By using bosonic systems, it is possible to enhance the performance of the quantum heat engine [26,27], and the power P is improved over a classical strategy.…”

Section: Introductionmentioning

confidence: 99%

Quantum-Enhanced Heat Engine Based on Superabsorption

Kamimura,

Hakoshima,

Matsuzaki

et al. 2021

Preprint

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Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence

Cited by 4 publications

References 0 publications

Asymptotic expansion of the solution of the master equation and its application to the speed limit

Asymptotic expansion of the solution of the master equation and its application to the speed limit

Thermodynamic uncertainty relations for coherently driven open quantum systems

Quantum-Enhanced Heat Engine Based on Superabsorption

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