1
|
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.
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
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.
Collapse
Affiliation(s)
- Takaaki Monnai
- Department of Science and Technology, Seikei University, Tokyo 180-8633, Japan
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Salamon P, Andresen B, Nulton J, Roach TNF, Rohwer F. More Stages Decrease Dissipation in Irreversible Step Processes. ENTROPY (BASEL, SWITZERLAND) 2023; 25:539. [PMID: 36981427 PMCID: PMC10048515 DOI: 10.3390/e25030539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 03/11/2023] [Accepted: 03/18/2023] [Indexed: 06/18/2023]
Abstract
The dissipation in an irreversible step process is reduced when the number of steps is increased in any refinement of the steps in the process. This is a consequence of the ladder theorem, which states that, for any irreversible process proceeding by a sequence of relaxations, dividing any relaxation step into two will result in a new sequence that is more efficient than the original one. This results in a more-steps-the-better rule, even when the new sequence of steps is not reoptimized. This superiority of many steps is well established empirically in, e.g., insulation and separation applications. In particular, the fact that the division of any step into two steps improves the overall efficiency has interesting implications for biological evolution and emphasizes thermodynamic length as a central measure for dissipation.
Collapse
Affiliation(s)
- Peter Salamon
- Department of Mathematics, San Diego State University, San Diego, CA 92182, USA;
| | - Bjarne Andresen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - James Nulton
- Department of Mathematics, San Diego State University, San Diego, CA 92182, USA;
| | - Ty N. F. Roach
- Department of Biology, San Diego State University, San Diego, CA 92182, USA; (T.N.F.R.); (F.R.)
| | - Forest Rohwer
- Department of Biology, San Diego State University, San Diego, CA 92182, USA; (T.N.F.R.); (F.R.)
| |
Collapse
|
6
|
Fundamental energy cost of finite-time parallelizable computing. Nat Commun 2023; 14:447. [PMID: 36707510 PMCID: PMC9883481 DOI: 10.1038/s41467-023-36020-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 01/11/2023] [Indexed: 01/28/2023] Open
Abstract
The fundamental energy cost of irreversible computing is given by the Landauer bound of [Formula: see text]/bit, where k is the Boltzmann constant and T is the temperature in Kelvin. However, this limit is only achievable for infinite-time processes. We here determine the fundamental energy cost of finite-time parallelizable computing within the framework of nonequilibrium thermodynamics. We apply these results to quantify the energetic advantage of parallel computing over serial computing. We find that the energy cost per operation of a parallel computer can be kept close to the Landauer limit even for large problem sizes, whereas that of a serial computer fundamentally diverges. We analyze, in particular, the effects of different degrees of parallelization and amounts of overhead, as well as the influence of non-ideal electronic hardware. We further discuss their implications in the context of current technology. Our findings provide a physical basis for the design of energy-efficient computers.
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
Scandi M, Barker D, Lehmann S, Dick KA, Maisi VF, Perarnau-Llobet M. Minimally Dissipative Information Erasure in a Quantum Dot via Thermodynamic Length. PHYSICAL REVIEW LETTERS 2022; 129:270601. [PMID: 36638287 DOI: 10.1103/physrevlett.129.270601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Revised: 11/29/2022] [Accepted: 12/12/2022] [Indexed: 06/17/2023]
Abstract
In this Letter, we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimization. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimize dissipation for slow protocols, with a bigger improvement as one approaches perfect erasure. Moreover, the geometric approach also leads to smaller dissipation even when the time of the protocol becomes comparable with the equilibration timescale of the system, i.e., away from the slow driving regime. Our results also illustrate, in a single-electron device, a fundamental principle of thermodynamic geometry: optimal finite-time thermodynamic protocols are those with constant dissipation rate along the process.
Collapse
Affiliation(s)
- Matteo Scandi
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - David Barker
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | - Sebastian Lehmann
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | - Kimberly A Dick
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
- Centre for Analysis and Synthesis, Lund University, Box 124, 22100 Lund, Sweden
| | - Ville F Maisi
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | | |
Collapse
|
9
|
Ma YH, Chen JF, Sun CP, Dong H. Minimal energy cost to initialize a bit with tolerable error. Phys Rev E 2022; 106:034112. [PMID: 36266886 DOI: 10.1103/physreve.106.034112] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Landauer's principle imposes a fundamental limit on the energy cost to perfectly initialize a classical bit, which is only reached under the ideal operation with infinitely long time. The question on the cost in the practical operation for a bit has been raised under the constraint by the finiteness of operation time. We discover a raise-up of energy cost by L^{2}(ε)/τ from the Landaeur's limit (k_{B}Tln2) for a finite-time τ initialization of a bit with an error probability ε. The thermodynamic length L(ε) between the states before and after initializing in the parametric space increases monotonously as the error decreases. For example, in the constant dissipation coefficient (γ_{0}) case, the minimal additional cost is 0.997k_{B}T/(γ_{0}τ) for ε=1% and 1.288k_{B}T/(γ_{0}τ) for ε=0.1%. Furthermore, the optimal protocol to reach the bound of minimal energy cost is proposed for the bit initialization realized via a finite-time isothermal process.
Collapse
Affiliation(s)
- Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
| | - Jin-Fu Chen
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
- Beijing Computational Science Research Center, Beijing 100193, China
- School of Physics, Peking University, Beijing, 100871, China
| | - C P Sun
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Hui Dong
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing, 100193, China
| |
Collapse
|
10
|
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.
Collapse
|
11
|
Chu Y, Cai J. Thermodynamic Principle for Quantum Metrology. PHYSICAL REVIEW LETTERS 2022; 128:200501. [PMID: 35657873 DOI: 10.1103/physrevlett.128.200501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Accepted: 04/28/2022] [Indexed: 06/15/2023]
Abstract
The heat dissipation in quantum metrology represents not only an unavoidable problem towards practical applications of quantum sensing devices but also a fundamental relationship between thermodynamics and quantum metrology. However, a general thermodynamic principle which governs the rule of energy consumption in quantum metrology, similar to Landauer's principle for heat dissipation in computations, has remained elusive. Here, we establish such a physical principle for energy consumption in order to achieve a certain level of measurement precision in quantum metrology, and show that it is intrinsically determined by the erasure of quantum Fisher information. The principle provides a powerful tool to investigate the advantage of quantum resources, not only in measurement precision but also in energy efficiency. It also serves as a bridge between thermodynamics and various fundamental physical concepts related in quantum physics and quantum information theory.
Collapse
Affiliation(s)
- Yaoming Chu
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China and Wuhan National High Magnetic Field Center, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jianming Cai
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China and Wuhan National High Magnetic Field Center, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
| |
Collapse
|
12
|
Hashimoto K, Uchiyama C. Effect of Quantum Coherence on Landauer’s Principle. ENTROPY 2022; 24:e24040548. [PMID: 35455211 PMCID: PMC9029971 DOI: 10.3390/e24040548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Revised: 03/30/2022] [Accepted: 03/30/2022] [Indexed: 11/16/2022]
Abstract
Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy (thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system–reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system–reservoir correlation, which may cause an additional source of energetic cost for the erasure.
Collapse
|
13
|
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.
Collapse
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
| |
Collapse
|
14
|
Zhen YZ, Egloff D, Modi K, Dahlsten O. Inverse linear versus exponential scaling of work penalty in finite-time bit reset. Phys Rev E 2022; 105:044147. [PMID: 35590656 DOI: 10.1103/physreve.105.044147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 04/04/2022] [Indexed: 06/15/2023]
Abstract
A bit reset is a basic operation in irreversible computing. This costs work and dissipates energy in the computer, creating a limit on speeds and energy efficiency of future irreversible computers. It was recently shown by Zhen et al. [Phys. Rev. Lett. 127, 190602 (2021)0031-900710.1103/PhysRevLett.127.190602] that for a finite-time reset protocol, the additional work on top of the quasistatic protocol can always be minimized by considering a two-level system, and then be lower bounded through a thermodynamical speed limit. An important question is to understand under what protocol parameters, including a bit reset error and maximum energy shift, this penalty decreases exponentially vs inverse linearly in the protocol time. Here we provide several analytical results to address this question, as well as numerical simulations of specific examples of protocols.
Collapse
Affiliation(s)
- Yi-Zheng Zhen
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Dario Egloff
- Institute of Theoretical Physics, Technical University Dresden, D-01062 Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Oscar Dahlsten
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| |
Collapse
|
15
|
Barker D, Scandi M, Lehmann S, Thelander C, Dick KA, Perarnau-Llobet M, Maisi VF. Experimental Verification of the Work Fluctuation-Dissipation Relation for Information-to-Work Conversion. PHYSICAL REVIEW LETTERS 2022; 128:040602. [PMID: 35148140 DOI: 10.1103/physrevlett.128.040602] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 11/23/2021] [Accepted: 12/22/2021] [Indexed: 06/14/2023]
Abstract
We study experimentally work fluctuations in a Szilard engine that extracts work from information encoded as the occupancy of an electron level in a semiconductor quantum dot. We show that as the average work extracted per bit of information increases toward the Landauer limit k_{B}Tln2, the work fluctuations decrease in accordance with the work fluctuation-dissipation relation. We compare the results to a protocol without measurement and feedback and show that when no information is used, the work output and fluctuations vanish simultaneously, contrasting the information-to-energy conversion case where increasing amount of work is produced with decreasing fluctuations. Our study highlights the importance of fluctuations in the design of information-to-work conversion processes.
Collapse
Affiliation(s)
- David Barker
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | - Matteo Scandi
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
| | - Sebastian Lehmann
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | - Claes Thelander
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| | - Kimberly A Dick
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
- Centre for Analysis and Synthesis, Lund University, Box 124, 22100 Lund, Sweden
| | | | - Ville F Maisi
- NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
| |
Collapse
|
16
|
Work Measurement in OPEN Quantum System. ENTROPY 2022; 24:e24020180. [PMID: 35205475 PMCID: PMC8871378 DOI: 10.3390/e24020180] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 01/04/2022] [Accepted: 01/12/2022] [Indexed: 12/10/2022]
Abstract
Work is an important quantity in thermodynamics. In a closed quanutm system, the two-point energy measurements can be applied to measure the work but cannot be utilized in an open quantum system. With the two-point energy measurements, it has been shown that the work fluctuation satisfies the Jarzynski equality. We propose a scheme to measure the work in an open quantum system through the technique of reservoir engineering. Based on this scheme, we show that the work fluctuation in open quantum system may violate the Jarzynski equality. We apply our scheme to a two-level atom coupled to an engineered reservoir and numerically justify the general results, especially demonstrating that the second law of thermodynamics can be violated.
Collapse
|
17
|
Van Vu T, Saito K. Finite-Time Quantum Landauer Principle and Quantum Coherence. PHYSICAL REVIEW LETTERS 2022; 128:010602. [PMID: 35061471 DOI: 10.1103/physrevlett.128.010602] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.
Collapse
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
| |
Collapse
|
18
|
Zhen YZ, Egloff D, Modi K, Dahlsten O. Universal Bound on Energy Cost of Bit Reset in Finite Time. PHYSICAL REVIEW LETTERS 2021; 127:190602. [PMID: 34797137 DOI: 10.1103/physrevlett.127.190602] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit in the framework of stochastic processes. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance.
Collapse
Affiliation(s)
- Yi-Zheng Zhen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Dario Egloff
- Institute of Theoretical Physics, Technische Universität Dresden, D-01062 Dresden, Germany
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Kavan Modi
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Oscar Dahlsten
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| |
Collapse
|
19
|
Thomsen K. Timelessness Strictly inside the Quantum Realm. ENTROPY (BASEL, SWITZERLAND) 2021; 23:772. [PMID: 34207444 PMCID: PMC8235759 DOI: 10.3390/e23060772] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 05/28/2021] [Accepted: 06/15/2021] [Indexed: 11/17/2022]
Abstract
Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only limited reality. Quantum systems, which we know, are embedded in the everyday classical world. Their preparation as well as their measurement-phases leave durable records and traces in the entropy of the environment. The Landauer Principle then gives a quantitative threshold for irreversibility. With double slit experiments and tunneling as paradigmatic examples, it is proposed that a label of timelessness offers clues for rendering a Copenhagen-type interpretation of quantum physics more "realistic" and acceptable by providing a coarse but viable link from the fundamental quantum realm to the classical world which humans directly experience.
Collapse
Affiliation(s)
- Knud Thomsen
- Paul Scherrer Institute (PSI), 5232 Villigen, Switzerland
| |
Collapse
|
20
|
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.
Collapse
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
| |
Collapse
|
21
|
Pires DP, Modi K, Céleri LC. Bounding generalized relative entropies: Nonasymptotic quantum speed limits. Phys Rev E 2021; 103:032105. [PMID: 33862799 DOI: 10.1103/physreve.103.032105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 02/16/2021] [Indexed: 06/12/2023]
Abstract
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of research areas. Remarkably, one of the key information-theoretic quantities is given by the relative entropy, which quantifies how difficult is to tell apart two probability distributions, or even two quantum states. Such a quantity rests at the core of fields like metrology, quantum thermodynamics, quantum communication, and quantum information. Given this broadness of applications, it is desirable to understand how this quantity changes under a quantum process. By considering a general unitary channel, we establish a bound on the generalized relative entropies (Rényi and Tsallis) between the output and the input of the channel. As an application of our bounds, we derive a family of quantum speed limits based on relative entropies. Possible connections between this family with thermodynamics, quantum coherence, asymmetry, and single-shot information theory are briefly discussed.
Collapse
Affiliation(s)
- Diego Paiva Pires
- International Institute of Physics and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil
| | - Kavan Modi
- School of Physics & Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Lucas Chibebe Céleri
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain
- Institute of Physics, Federal University of Goiás, 74.690-900 Goiânia, Goiás, Brazil
| |
Collapse
|
22
|
Van Vu T, Hasegawa Y. Geometrical Bounds of the Irreversibility in Markovian Systems. PHYSICAL REVIEW LETTERS 2021; 126:010601. [PMID: 33480766 DOI: 10.1103/physrevlett.126.010601] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 11/03/2020] [Accepted: 12/03/2020] [Indexed: 06/12/2023]
Abstract
We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from below by a modified Wasserstein distance between the initial and final states, thus strengthening the Clausius inequality in the reversible-Markov case. The modified metric can be regarded as a discrete-state generalization of the Wasserstein metric, which has been used to bound dissipation in continuous-state Langevin systems. Notably, the derived bounds can be interpreted as the quantum and classical speed limits, implying that the associated entropy production constrains the minimum time of transforming a system state. We illustrate the results on several systems and show that a tighter bound than the Carnot bound for the efficiency of quantum heat engines can be obtained.
Collapse
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
| |
Collapse
|