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Shastri R, Venkatesh BP. Controlling work output and coherence in finite-time quantum Otto engines through monitoring. Phys Rev E 2024; 109:014102. [PMID: 38366526 DOI: 10.1103/physreve.109.014102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 12/01/2023] [Indexed: 02/18/2024]
Abstract
We examine the role of diagnostic quantum measurements on the work statistics of a finite-time quantum Otto heat engine operated in the steady state. We consider three pointer-based measurement schemes that differ in the number of system-pointer interactions and pointer measurements. We show that the coherence of the working substance and the work output of the engine can be controlled by tuning the monitoring measurements. Moreover, for a working substance consisting of a two-level system we show that while all three schemes reproduce the predictions of the cycle without any monitoring for the average work in the limit of infinitely weak measurement, only two of the schemes can reproduce the two-point projective measurement results in the limit of strong measurement.
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Affiliation(s)
- Rahul Shastri
- Indian Institute of Technology Gandhinagar, Palaj, Gujarat 382055, India
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2
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Nakajima S, Utsumi Y. Symmetric-logarithmic-derivative Fisher information for kinetic uncertainty relations. Phys Rev E 2023; 108:054136. [PMID: 38115464 DOI: 10.1103/physreve.108.054136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 11/08/2023] [Indexed: 12/21/2023]
Abstract
We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a quantum kinetic uncertainty relation derived by Vu and Saito [Phys. Rev. Lett. 128, 140602 (2022)0031-900710.1103/PhysRevLett.128.140602], the Fisher information of probability of quantum trajectory with a time-rescaling parameter plays an essential role. This Fisher information is upper bounded by the SLD Fisher information. For a finite time and arbitrary initial state, we derive a concise expression of the SLD Fisher information, which is a double time integral and can be calculated by solving coupled first-order differential equations. We also derive a simple lower bound of the Fisher information of quantum trajectory. We point out that the SLD Fisher information also appears in the speed limit based on the Mandelstam-Tamm relation by Hasegawa [Nat. Commun. 14, 2828 (2023)2041-172310.1038/s41467-023-38074-8]. When the jump operators connect eigenstates of the system Hamiltonian, we show that the Bures angle in the interaction picture is upper bounded by the square root of the dynamical activity at short times, which contrasts with the classical counterpart.
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Affiliation(s)
- Satoshi Nakajima
- Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan
| | - Yasuhiro Utsumi
- Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mie 514-8507, Japan
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Das A, Mahunta S, Agarwalla BK, Mukherjee V. Precision bound and optimal control in periodically modulated continuous quantum thermal machines. Phys Rev E 2023; 108:014137. [PMID: 37583225 DOI: 10.1103/physreve.108.014137] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 07/07/2023] [Indexed: 08/17/2023]
Abstract
We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.
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Affiliation(s)
- Arpan Das
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Shishira Mahunta
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research Pune, Pune 411008, India
| | - Victor Mukherjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
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Bettmann LP, Kewming MJ, Goold J. Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework. Phys Rev E 2023; 107:044102. [PMID: 37198837 DOI: 10.1103/physreve.107.044102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 03/14/2023] [Indexed: 05/19/2023]
Abstract
Understanding the thermodynamic role of measurement in quantum mechanical systems is a burgeoning field of study. In this article, we study a double quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We assume that the DQD is continuously monitored by a quantum point contact (QPC), which serves as a charge detector. Starting from a minimalist microscopic model for the QPC and reservoirs, we show that the local master equation of the DQD can alternatively be derived in the framework of repeated interactions and that this framework guarantees a thermodynamically consistent description of the DQD and its environment (including the QPC). We analyze the effect of the measurement strength and identify a regime in which particle transport through the DQD is both assisted and stabilized by dephasing. We also find that in this regime the entropic cost of driving the particle current with fixed relative fluctuations through the DQD is reduced. We thus conclude that under continuous measurement a more constant particle current may be achieved at a fixed entropic cost.
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Affiliation(s)
| | - Michael J Kewming
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
| | - John Goold
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
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Souza LDS, Manzano G, Fazio R, Iemini F. Collective effects on the performance and stability of quantum heat engines. Phys Rev E 2022; 106:014143. [PMID: 35974546 DOI: 10.1103/physreve.106.014143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.
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Affiliation(s)
- Leonardo da Silva Souza
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, Brazil
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos 6627, Belo Horizonte Minas Gerais 31270-901, Brazil
| | - Gonzalo Manzano
- Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Rosario Fazio
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151, Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Naples, Italy
| | - Fernando Iemini
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, Brazil
- International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151, Trieste, Italy
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Ptaszyński K. Non-Markovian thermal operations boosting the performance of quantum heat engines. Phys Rev E 2022; 106:014114. [PMID: 35974499 DOI: 10.1103/physreve.106.014114] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.
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Affiliation(s)
- Krzysztof Ptaszyński
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
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Van Vu T, Saito K. Thermodynamics of Precision in Markovian Open Quantum Dynamics. PHYSICAL REVIEW LETTERS 2022; 128:140602. [PMID: 35476476 DOI: 10.1103/physrevlett.128.140602] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Revised: 03/02/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.
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Affiliation(s)
- Tan Van Vu
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
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Singh D, Hyeon C. Origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system. Phys Rev E 2021; 104:054115. [PMID: 34942793 DOI: 10.1103/physreve.104.054115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 11/02/2021] [Indexed: 11/07/2022]
Abstract
Thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the tradeoff between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities. In a series of efforts to extend the relation to the one under more generalized conditions, it has been noticed that the bound is less tight in open quantum processes. To study the origin of the loose bounds, we consider an external field-driven transition dynamics of a two-level quantum system weakly coupled to the bosonic bath as a model of an open quantum system. The model makes it explicit that the imaginary part of quantum coherence, which contributes to dissipation to the environment, is responsible for loosening the TUR bound by suppressing the relative fluctuations in the irreversible current of transitions, whereas the real part of the coherence tightens it. Our study offers a better understanding of how quantum nature affects the TUR bound.
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Kalaee AAS, Wacker A, Potts PP. Violating the thermodynamic uncertainty relation in the three-level maser. Phys Rev E 2021; 104:L012103. [PMID: 34412265 DOI: 10.1103/physreve.104.l012103] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2021] [Accepted: 06/29/2021] [Indexed: 12/15/2022]
Abstract
Nanoscale heat engines are subject to large fluctuations which affect their precision. The thermodynamic uncertainty relation (TUR) provides a trade-off between output power, fluctuations, and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This Letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil-Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres to a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model are not uncommon.
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Affiliation(s)
| | - Andreas Wacker
- Mathematical Physics and NanoLund, Lund University, Box 118, 221 00 Lund, Sweden
| | - Patrick P Potts
- Mathematical Physics and NanoLund, Lund University, Box 118, 221 00 Lund, Sweden.,Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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Liu J, Segal D. Coherences and the thermodynamic uncertainty relation: Insights from quantum absorption refrigerators. Phys Rev E 2021; 103:032138. [PMID: 33862758 DOI: 10.1103/physreve.103.032138] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a tradeoff relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where nonzero coherence between eigenstates can either suppress or enhance the cooling power, compared with the incoherent limit. In either scenario, we find enhanced relative noise of the cooling power (standard deviation of the power over the mean) in the presence of system coherence, thereby corroborating the thermodynamic uncertainty relation. Our results indicate that fluctuations necessitate consideration when assessing the performance of quantum coherent thermal machines.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, M5S 3H6, Canada
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, M5S 3H6, Canada.,Department of Physics, 60 Saint George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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