1
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Guarnieri G, Eisert J, Miller HJD. Generalized Linear Response Theory for the Full Quantum Work Statistics. PHYSICAL REVIEW LETTERS 2024; 133:070405. [PMID: 39213553 DOI: 10.1103/physrevlett.133.070405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 06/17/2024] [Indexed: 09/04/2024]
Abstract
We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study nonequilibrium fluctuations in complex quantum systems. Our results establish a number of refined quantum thermodynamic constraints on the work statistics that apply to regimes of perturbative but arbitrarily fast protocols, and do not rely on assumptions such as slow driving or weak coupling. Finally, our approach uncovers a distinctly quantum signature in the work statistics that originates from underlying zero-point energy fluctuations. This causes an increased dispersion of the probability distribution at short driving times, a feature that can be probed in efforts to witness nonclassical effects in quantum thermodynamics.
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2
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Onishchenko O, Guarnieri G, Rosillo-Rodes P, Pijn D, Hilder J, Poschinger UG, Perarnau-Llobet M, Eisert J, Schmidt-Kaler F. Probing coherent quantum thermodynamics using a trapped ion. Nat Commun 2024; 15:6974. [PMID: 39143048 PMCID: PMC11324868 DOI: 10.1038/s41467-024-51263-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 08/02/2024] [Indexed: 08/16/2024] Open
Abstract
Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, where coherence and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we demonstrate the possibility to experimentally measure and benchmark a genuine quantum correction, induced by quantum friction, to the classical work fluctuation-dissipation relation. This is achieved by combining laser-induced coherent Hamiltonian rotations and energy measurements on a trapped ion. Our results demonstrate that recent developments in stochastic quantum thermodynamics can be used to benchmark and unambiguously distinguish genuine quantum coherent signatures generated along driving protocols, even in presence of experimental SPAM errors and, most importantly, beyond the regimes for which theoretical predictions are available (e.g., in slow driving).
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Affiliation(s)
- O Onishchenko
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany
| | - G Guarnieri
- Department of Physics and INFN - Sezione di Pavia, University of Pavia, Via Bassi 6, 27100, Pavia, Italy.
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany.
| | - P Rosillo-Rodes
- Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat de les Illes Balears, E-07122, Palma, Spain
| | - D Pijn
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany
| | - J Hilder
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany
| | - U G Poschinger
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany
| | - M Perarnau-Llobet
- Department of Applied Physics, University of Geneva, 1211, Geneva, Switzerland
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany
| | - F Schmidt-Kaler
- QUANTUM, Institut für Physik, Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany
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3
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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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4
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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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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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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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7
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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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8
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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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9
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Erdman PA, Noé F. Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning. PNAS NEXUS 2023; 2:pgad248. [PMID: 37593201 PMCID: PMC10427747 DOI: 10.1093/pnasnexus/pgad248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 07/13/2023] [Accepted: 07/25/2023] [Indexed: 08/19/2023]
Abstract
A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on reinforcement learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal tradeoffs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.
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Affiliation(s)
- Paolo A Erdman
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Microsoft Research AI4Science, Karl-Liebknecht Str. 32, 10178 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, TX 77005, USA
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10
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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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11
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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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12
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Arrachea L. Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:036501. [PMID: 36603220 DOI: 10.1088/1361-6633/acb06b] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 01/05/2023] [Indexed: 06/17/2023]
Abstract
We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.
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Affiliation(s)
- Liliana Arrachea
- Escuela de Ciencia y Tecnología and ICIFI, Universidad de San Martín, Av. 25 de Mayo y Francia, 1650 Buenos Aires, Argentina
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13
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Bhandari B, Czupryniak R, Erdman PA, Jordan AN. Measurement-Based Quantum Thermal Machines with Feedback Control. ENTROPY (BASEL, SWITZERLAND) 2023; 25:204. [PMID: 36832571 PMCID: PMC9955564 DOI: 10.3390/e25020204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Revised: 01/13/2023] [Accepted: 01/16/2023] [Indexed: 06/18/2023]
Abstract
We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.
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Affiliation(s)
- Bibek Bhandari
- Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
| | - Robert Czupryniak
- Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, NY 14627, USA
| | - Paolo Andrea Erdman
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Andrew N. Jordan
- Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
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14
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Koyuk T, Seifert U. Thermodynamic Uncertainty Relation in Interacting Many-Body Systems. PHYSICAL REVIEW LETTERS 2022; 129:210603. [PMID: 36461951 DOI: 10.1103/physrevlett.129.210603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 06/01/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.
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Affiliation(s)
- Timur Koyuk
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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15
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Liu F. Semi-Markov processes in open quantum systems: Connections and applications in counting statistics. Phys Rev E 2022; 106:054152. [PMID: 36559413 DOI: 10.1103/physreve.106.054152] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the semi-Markov processes is also proposed. In addition to inheriting all statistical properties possessed by the piecewise deterministic processes of wave functions, the semi-Markov processes show their unique advantages in quantum counting statistics. Compared with the conventional method of the tilted quantum master equation, they can be applied to more general counting quantities. In particular, the terms involved in the method have precise probability meanings. We use a driven two-level quantum system to exemplify these results.
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Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
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16
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Liu J, Jung KA. Optimal linear cyclic quantum heat engines cannot benefit from strong coupling. Phys Rev E 2022; 106:L022105. [PMID: 36109930 DOI: 10.1103/physreve.106.l022105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 08/15/2022] [Indexed: 06/15/2023]
Abstract
Uncovering whether strong system-bath coupling can be an advantageous operation resource for energy conversion can facilitate the development of efficient quantum heat engines (QHEs). Yet, a consensus on this ongoing debate is still lacking owing to challenges arising from treating strong couplings. Here, we conclude the debate for optimal linear cyclic QHEs operated under a small temperature difference by revealing the detrimental role of strong system-bath coupling in their optimal operations. We analytically demonstrate that both the efficiency at maximum power and maximum efficiency of strong-coupling linear cyclic QHEs are upper bounded by their weak-coupling counterparts with the same degree of time-reversal symmetry breaking. Under strong time-reversal symmetry breaking, we further reveal a quadratic suppression of the optimal efficiencies relative to the Carnot limit when away from the weak-coupling regime, along with a quadratic enhancement of the mean entropy production rate.
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Affiliation(s)
- Junjie Liu
- Department of Physics, International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China
| | - Kenneth A Jung
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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17
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Giri SK, Goswami HP. Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings. Phys Rev E 2022; 106:024131. [PMID: 36109996 DOI: 10.1103/physreve.106.024131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
External driving of bath temperatures with a phase difference of a nonequilibrium quantum engine leads to the emergence of geometric effects on the thermodynamics. In this work we modulate the amplitude of the external driving protocols by introducing envelope functions and study the role of geometric effects on the flux, noise, and efficiency of a four-level driven quantum heat engine coupled with two thermal baths and a unimodal cavity. We observe that having a finite width of the modulation envelope introduces an additional control knob for studying the thermodynamics in the adiabatic limit. The optimization of the flux as well as the noise with respect to thermally induced quantum coherences becomes possible in the presence of geometric effects, which hitherto has not been possible with sinusoidal driving without an envelope. We also report the deviation of the slope and generation of an intercept in the standard expression for efficiency at maximum power as a function of Carnot efficiency in the presence of geometric effects under the amplitude modulation. Further, a recently developed universal bound on the efficiency obtained from the thermodynamic uncertainty relation is shown not to hold when a small width of the modulation envelope along with a large value of cavity temperature is maintained.
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Affiliation(s)
- Sajal Kumar Giri
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA
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18
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Verification of Information Thermodynamics in a Trapped Ion System. ENTROPY 2022; 24:e24060813. [PMID: 35741534 PMCID: PMC9222944 DOI: 10.3390/e24060813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Revised: 06/07/2022] [Accepted: 06/08/2022] [Indexed: 02/05/2023]
Abstract
Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.
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19
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Frim AG, DeWeese MR. Geometric Bound on the Efficiency of Irreversible Thermodynamic Cycles. PHYSICAL REVIEW LETTERS 2022; 128:230601. [PMID: 35749204 DOI: 10.1103/physrevlett.128.230601] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
Stochastic thermodynamics has revolutionized our understanding of heat engines operating in finite time. Recently, numerous studies have considered the optimal operation of thermodynamic cycles acting as heat engines with a given profile in thermodynamic space (e.g., P-V space in classical thermodynamics), with a particular focus on the Carnot engine. In this work, we use the lens of thermodynamic geometry to explore the full space of thermodynamic cycles with continuously varying bath temperature in search of optimally shaped cycles acting in the slow-driving regime. We apply classical isoperimetric inequalities to derive a universal geometric bound on the efficiency of any irreversible thermodynamic cycle and explicitly construct efficient heat engines operating in finite time that nearly saturate this bound for a specific model system. Given the bound, these optimal cycles perform more efficiently than all other thermodynamic cycles operating as heat engines in finite time, including notable cycles, such as those of Carnot, Stirling, and Otto. For example, in comparison to recent experiments, this corresponds to orders of magnitude improvement in the efficiency of engines operating in certain time regimes. Our results suggest novel design principles for future mesoscopic heat engines and are ripe for experimental investigation.
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Affiliation(s)
- Adam G Frim
- Department of Physics, University of California, Berkeley, Berkeley, California, 94720
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California, 94720
- Redwood Center For Theoretical Neuroscience, University of California, Berkeley, Berkeley, California, 94720
- Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California, 94720
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20
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Eglinton J, Brandner K. Geometric bounds on the power of adiabatic thermal machines. Phys Rev E 2022; 105:L052102. [PMID: 35706185 DOI: 10.1103/physreve.105.l052102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
We analyze the performance of slowly driven meso- and microscale refrigerators and heat engines that operate between two thermal baths with a small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasistatic limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.
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Affiliation(s)
- Joshua Eglinton
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Kay Brandner
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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21
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Frim AG, DeWeese MR. Optimal finite-time Brownian Carnot engine. Phys Rev E 2022; 105:L052103. [PMID: 35706186 DOI: 10.1103/physreve.105.l052103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 04/29/2022] [Indexed: 06/15/2023]
Abstract
Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time nonequilibrium cyclic operation of the parametric harmonic oscillator in contact with a time-varying heat bath with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20% improvement in dissipated energy over previous experimentally tested protocols and a ∼50% improvement under other conditions for one of our engines, whereas our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.
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Affiliation(s)
- Adam G Frim
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
- Redwood Center For Theoretical Neuroscience, University of California, Berkeley, Berkeley, California 94720, USA
- Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, California 94720, USA
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22
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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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23
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Yan LL, Zhang JW, Yun MR, Li JC, Ding GY, Wei JF, Bu JT, Wang B, Chen L, Su SL, Zhou F, Jia Y, Liang EJ, Feng M. Experimental Verification of Dissipation-Time Uncertainty Relation. PHYSICAL REVIEW LETTERS 2022; 128:050603. [PMID: 35179926 DOI: 10.1103/physrevlett.128.050603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Revised: 11/08/2021] [Accepted: 01/14/2022] [Indexed: 06/14/2023]
Abstract
Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.
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Affiliation(s)
- L-L Yan
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-W Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - M-R Yun
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-C Li
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - G-Y Ding
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - J-F Wei
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - J-T Bu
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - B Wang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
| | - L Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - S-L Su
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - F Zhou
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
| | - Y Jia
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
- Key Laboratory for Special Functional Materials of Ministry of Education, and School of Materials and Engineering, Henan University, Kaifeng 475001, China
| | - E-J Liang
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - M Feng
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- School of Physics, University of the Chinese Academy of Sciences, Beijing 100049, China
- Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Technology, Guangzhou 511458, China
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24
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Saryal S, Mohanta S, Agarwalla BK. Bounds on fluctuations for machines with broken time-reversal symmetry: A linear response study. Phys Rev E 2022; 105:024129. [PMID: 35291179 DOI: 10.1103/physreve.105.024129] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator, or pump, is imposed on both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio between fluctuations of output and input current are obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relations for time-reversal symmetry-broken systems. We illustrate these findings for two different types of machines: (1) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field and (2) a periodically driven classical Brownian heat engine.
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Affiliation(s)
- Sushant Saryal
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Sandipan Mohanta
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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25
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Hasegawa Y. Irreversibility, Loschmidt Echo, and Thermodynamic Uncertainty Relation. PHYSICAL REVIEW LETTERS 2021; 127:240602. [PMID: 34951787 DOI: 10.1103/physrevlett.127.240602] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 10/28/2021] [Indexed: 06/14/2023]
Abstract
Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by the Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.
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Affiliation(s)
- Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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26
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Shpielberg O, Pal A. Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies. Phys Rev E 2021; 104:064141. [PMID: 35030838 DOI: 10.1103/physreve.104.064141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 12/02/2021] [Indexed: 06/14/2023]
Abstract
A universal large N theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse-grained thermodynamic uncertainty relations-one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly useful in the many-body regime, where typically a coarse-grained approach is required to handle the large microscopic state space.
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Affiliation(s)
- Ohad Shpielberg
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
| | - Arnab Pal
- Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University & Department of Physics, Indian Institute of Technology, Kanpur, Kanpur 208016, India
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27
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Van Vu T, Hasegawa Y. Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2021; 127:190601. [PMID: 34797124 DOI: 10.1103/physrevlett.127.190601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 10/04/2021] [Indexed: 06/13/2023]
Abstract
We consider the thermal relaxation process of a quantum system attached to single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower bounded by a relative entropy between the unitarily evolved state and the final state. The bound characterizes the state discrepancy induced by the nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.
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Affiliation(s)
- Tan Van Vu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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28
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Miller HJD, Mohammady MH, Perarnau-Llobet M, Guarnieri G. Joint statistics of work and entropy production along quantum trajectories. Phys Rev E 2021; 103:052138. [PMID: 34134351 DOI: 10.1103/physreve.103.052138] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 04/30/2021] [Indexed: 11/07/2022]
Abstract
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, then we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.
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Affiliation(s)
- Harry J D Miller
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - M Hamed Mohammady
- RCQI, Institute of Physics, Slovak Academy of Sciences, Bratislava 84511, Slovakia
| | | | - Giacomo Guarnieri
- School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland.,Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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