1
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Bourgeois J, Blasi G, Khandelwal S, Haack G. Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations. ENTROPY (BASEL, SWITZERLAND) 2024; 26:497. [PMID: 38920506 PMCID: PMC11203105 DOI: 10.3390/e26060497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Revised: 05/29/2024] [Accepted: 06/03/2024] [Indexed: 06/27/2024]
Abstract
Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.
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Affiliation(s)
- Jeanne Bourgeois
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Gianmichele Blasi
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Shishir Khandelwal
- Physics Department, Lund University, Box 118, 22100 Lund, Sweden
- NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - Géraldine Haack
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
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2
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Wang Z, Ren J. Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport. PHYSICAL REVIEW LETTERS 2024; 132:207101. [PMID: 38829089 DOI: 10.1103/physrevlett.132.207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 09/06/2023] [Accepted: 04/11/2024] [Indexed: 06/05/2024]
Abstract
Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.
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Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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3
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Salazar DSP. Uncertainty relation for symmetric Petz-Rényi relative entropy. Phys Rev E 2024; 109:L052106. [PMID: 38907441 DOI: 10.1103/physreve.109.l052106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 04/23/2024] [Indexed: 06/24/2024]
Abstract
Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace distance in evaluating their similarity. This fidelity is bounded by a function of the trace distance, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace distance. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace distance, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics.
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4
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Farina D, Benazout B, Centrone F, Acín A. Thermodynamic precision in the nonequilibrium exchange scenario. Phys Rev E 2024; 109:034112. [PMID: 38632747 DOI: 10.1103/physreve.109.034112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 01/22/2024] [Indexed: 04/19/2024]
Abstract
We discuss exchange scenario thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In this way we investigate the use of entangled nonequilibrium steady states as end points of thermodynamic cycles. In this framework we prove analytically that for a paradigmatic unitary it is possible to construct an exchange scenario thermodynamic uncertainty relation. However, despite holding in many cases, we also show that such a relation ceases to be valid when considering other suitable unitary quenches. Furthermore, this paradigmatic example allows us to shed light on the role of the entanglement between the two qubits for precise work absorption. By considering the projection of the entangled steady state onto the set of separable states, we provide examples where such projection implies an increase of the relative uncertainty, showing the usefulness of entanglement.
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Affiliation(s)
- Donato Farina
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- Physics Department E. Pancini, Università degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Naples, Italy
| | - Bilal Benazout
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- Physics Department, Ecole Normale Supérieure, Université PSL, 24 rue Lhomond 75005 Paris, France
| | - Federico Centrone
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
| | - Antonio Acín
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain
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5
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Salazar DSP. Quantum relative entropy uncertainty relation. Phys Rev E 2024; 109:L012103. [PMID: 38366413 DOI: 10.1103/physreve.109.l012103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.
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Affiliation(s)
- Domingos S P Salazar
- Unidade de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco, Brazil
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6
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Meier F, Schwarzhans E, Erker P, Huber M. Fundamental Accuracy-Resolution Trade-Off for Timekeeping Devices. PHYSICAL REVIEW LETTERS 2023; 131:220201. [PMID: 38101372 DOI: 10.1103/physrevlett.131.220201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 07/28/2023] [Accepted: 10/09/2023] [Indexed: 12/17/2023]
Abstract
From a thermodynamic point of view, all clocks are driven by irreversible processes. Additionally, one can use oscillatory systems to temporally modulate the thermodynamic flux towards equilibrium. Focusing on the most elementary thermalization events, this modulation can be thought of as a temporal probability concentration for these events. There are two fundamental factors limiting the performance of clocks: On the one level, the inevitable drifts of the oscillatory system, which are addressed by finding stable atomic or nuclear transitions that lead to astounding precision of today's clocks. On the other level, there is the intrinsically stochastic nature of the irreversible events upon which the clock's operation is based. This becomes relevant when seeking to maximize a clock's resolution at high accuracy, which is ultimately limited by the number of such stochastic events per reference time unit. We address this essential trade-off between clock accuracy and resolution, proving a universal bound for all clocks whose elementary thermalization events are memoryless.
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Affiliation(s)
- Florian Meier
- Vienna Center for Quantum Science and Technology, Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Emanuel Schwarzhans
- Vienna Center for Quantum Science and Technology, Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
| | - Paul Erker
- Vienna Center for Quantum Science and Technology, Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 1090 Vienna, Austria
| | - Marcus Huber
- Vienna Center for Quantum Science and Technology, Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 1090 Vienna, Austria
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7
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Chesi G, Macchiavello C, Sacchi MF. Work Fluctuations in Ergotropic Heat Engines. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1528. [PMID: 37998220 PMCID: PMC10670664 DOI: 10.3390/e25111528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Revised: 11/02/2023] [Accepted: 11/04/2023] [Indexed: 11/25/2023]
Abstract
We study the work fluctuations in ergotropic heat engines, namely two-stroke quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exhaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non-trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3=U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs), which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.
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Affiliation(s)
- Giovanni Chesi
- National Institute for Nuclear Physics, Sezione di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy;
| | - Chiara Macchiavello
- National Institute for Nuclear Physics, Sezione di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy;
- QUIT Group, Dipartimento di Fisica, Università degli Studi di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy;
| | - Massimiliano Federico Sacchi
- QUIT Group, Dipartimento di Fisica, Università degli Studi di Pavia, Via Agostino Bassi 6, 27100 Pavia, Italy;
- CNR-Istituto di Fotonica e Nanotecnologie, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
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8
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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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9
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Ray KJ, Boyd AB, Guarnieri G, Crutchfield JP. Thermodynamic uncertainty theorem. Phys Rev E 2023; 108:054126. [PMID: 38115447 DOI: 10.1103/physreve.108.054126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 09/11/2023] [Indexed: 12/21/2023]
Abstract
Thermodynamic uncertainty relations (TURs) express a fundamental lower bound on the precision (inverse scaled variance) of any thermodynamic charge-e.g., work or heat-by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend TUR inequalities by incorporating and analyzing the impact of higher statistical cumulants of the entropy production itself within the general framework of time-symmetrically-controlled computation. We derive an exact expression for the charge that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name the thermodynamic uncertainty theorem (TUT). Importantly, both the minimum scaled variance charge and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any charge's precision. This is made explicit via a thorough numerical analysis of "swap" and "reset" computations that quantitatively compares the TUT against previous generalized TURs.
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Affiliation(s)
- Kyle J Ray
- Complexity Sciences Center and Department of Physics and Astronomy, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - Alexander B Boyd
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
- School of Physics, Trinity College Dublin, College Green, Dublin 2, D02 PN40, Ireland
| | - Giacomo Guarnieri
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics and Astronomy, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
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10
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Monnai T. Arbitrary-time thermodynamic uncertainty relation from fluctuation theorem. Phys Rev E 2023; 108:024119. [PMID: 37723688 DOI: 10.1103/physreve.108.024119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 07/13/2023] [Indexed: 09/20/2023]
Abstract
The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer, for example, for a class of continuous-time stochastic processes. However, its extension to general nonequilibrium dynamics is still an unsolved problem. We derive TUR for an arbitrary finite time from exchange fluctuation theorem under a geometric necessary and sufficient condition. We also generally show a necessary and sufficient condition of multidimensional TUR in a unified manner. As a nontrivial practical consequence, we obtain universal scaling relations among the mean and variance of the charge transfer in short time regime. In this manner, we can deepen our understanding of a link between two important rigorous relations, i.e., the fluctuation theorem and the thermodynamic uncertainty relation.
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Affiliation(s)
- Takaaki Monnai
- Department of Science and Technology, Seikei University, Tokyo 180-8633, Japan
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11
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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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12
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Lucena IRAC, Batista RA, Ramos JGGS. Thermodynamic uncertainty relations in mesoscopic devices. Phys Rev E 2023; 107:064104. [PMID: 37464637 DOI: 10.1103/physreve.107.064104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 05/15/2023] [Indexed: 07/20/2023]
Abstract
We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).
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Affiliation(s)
- I R A C Lucena
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 Joaão Pessoa, Paraíba, Brazil
| | - R A Batista
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 Joaão Pessoa, Paraíba, Brazil
| | - J G G S Ramos
- Departamento de Física, Universidade Federal da Paraíba, 58051-970 Joaão Pessoa, Paraíba, Brazil
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13
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Gerry M, Segal D. Full counting statistics and coherences: Fluctuation symmetry in heat transport with the unified quantum master equation. Phys Rev E 2023; 107:054115. [PMID: 37329000 DOI: 10.1103/physreve.107.054115] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
Recently, a "unified" quantum master equation was derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equation describes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equation to investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equation gives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equation to those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.
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Affiliation(s)
- Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
- Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6, Canada
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14
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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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15
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Van Vu T, Saito K. Topological Speed Limit. PHYSICAL REVIEW LETTERS 2023; 130:010402. [PMID: 36669213 DOI: 10.1103/physrevlett.130.010402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Revised: 11/15/2022] [Accepted: 12/05/2022] [Indexed: 06/17/2023]
Abstract
Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.
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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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