1
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Mohammadi A, Shafiee A. Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process. Phys Chem Chem Phys 2024; 26:3990-3999. [PMID: 38224013 DOI: 10.1039/d3cp04528e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energies. Using the latter, we investigate the evolution of extractable work when an open quantum system undergoes a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way that the first and the second law of thermodynamics are combined. We then identify the contributions from the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the evolution of heat and extractable work of the open quantum system. Furthermore, we show how this correspondence between irreversibility and extractable work has the potential to provide a clear explanation of how the quantum properties of a system affect its extractable work evolution. Specifically, we establish this by directly connecting the change in extractable work with the change in standard quantifiers of quantum non-Markovianity and quantum coherence during a general quantum process. We illustrate these results with two examples.
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Affiliation(s)
- Amin Mohammadi
- Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran.
| | - Afshin Shafiee
- Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran.
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2
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Hohm U, Schiller C. Testing the Minimum System Entropy and the Quantum of Entropy. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1511. [PMID: 37998203 PMCID: PMC10670145 DOI: 10.3390/e25111511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2023] [Revised: 10/25/2023] [Accepted: 10/31/2023] [Indexed: 11/25/2023]
Abstract
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.
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Affiliation(s)
- Uwe Hohm
- Institut für Physikalische und Theoretische Chemie, Technische Universität Braunschweig, Gaußstr. 17, 38106 Braunschweig, Germany
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3
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Gu J. Speed limit, dissipation bound, and dissipation-time trade-off in thermal relaxation processes. Phys Rev E 2023; 108:L052103. [PMID: 38115476 DOI: 10.1103/physreve.108.l052103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 10/15/2023] [Indexed: 12/21/2023]
Abstract
We investigate bounds on speed, nonadiabatic entropy production, and the trade-off relation between them for classical stochastic processes with time-independent transition rates. Our results show that the time required to evolve from an initial to a desired target state is bounded from below by the information-theoretical ∞-Rényi divergence between these states, divided by the total rate. Furthermore, we conjecture and provide extensive numerical evidence for an information-theoretical bound on the nonadiabatic entropy production and a dissipation-time trade-off relation that outperforms previous bounds in some cases..
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Affiliation(s)
- Jie Gu
- Chengdu Academy of Education Sciences, Chengdu 610036, China
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4
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de Assis RJ, Diniz CM, de Almeida NG, Villas-Bôas CJ. Thermodynamics of the Ramsey Zone. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1430. [PMID: 37895551 PMCID: PMC10605998 DOI: 10.3390/e25101430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Revised: 09/28/2023] [Accepted: 10/06/2023] [Indexed: 10/29/2023]
Abstract
We studied the thermodynamic properties such as the entropy, heat (JQ), and work (JW) rates involved when an atom passes through a Ramsey zone, which consists of a mode field inside a low-quality factor cavity that behaves classically, promoting rotations on the atomic state. Focusing on the atom, we show that JW predominates when the atomic rotations are successful, maintaining its maximum purity as computed by the von Neumann entropy. Conversely, JQ stands out when the atomic state ceases to be pure due to its entanglement with the cavity mode. With this, we interpret the quantum-to-classical transition in light of the heat and work rates. Besides, we show that, for the cavity mode to work as a Ramsey zone (classical field), several photons (of the order of 106) need to cross the cavity, which explains its classical behavior, even when the inside average number of photons is of the order of unity.
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Affiliation(s)
- Rogério Jorge de Assis
- Instituto de Física, Universidade Federal de Goiás, Goiânia 74690-900, GO, Brazil;
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
| | - Ciro Micheletti Diniz
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
| | | | - Celso Jorge Villas-Bôas
- Departamento de Física, Universidade Federal de São Carlos, São Carlos 13565-905, SP, Brazil; (C.M.D.); (C.J.V.-B.)
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5
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Kallush S, Dann R, Kosloff R. Controlling the uncontrollable: Quantum control of open-system dynamics. SCIENCE ADVANCES 2022; 8:eadd0828. [PMID: 36322661 PMCID: PMC9629718 DOI: 10.1126/sciadv.add0828] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
Control of open quantum systems is essential for the realization of contemporary quantum science and technology. We demonstrate such control using a thermodynamically consistent framework, taking into account the fact that the drive can modify the system's interaction with the environment. Such an effect is incorporated within the dynamical equation, leading to control-dependent dissipation. This relation serves as the key element for open-system control. The control paradigm is displayed by analyzing entropy-changing state-to-state transformations, such as heating and cooling. The difficult task of controlling quantum gates is achieved for nonunitary reset maps with complete memory loss. In addition, we identify a mechanism for controlling unitary gates by actively removing entropy from the system to the environment. We demonstrate a universal set of single- and double-qubit unitary gates under dissipation.
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Affiliation(s)
- Shimshon Kallush
- Sciences Department, Holon Academic Institute of Technology, 52 Golomb Street, Holon 58102, Israel
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Roie Dann
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Ronnie Kosloff
- The Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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6
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Cerisola F, Sapienza F, Roncaglia AJ. Heat engines with single-shot deterministic work extraction. Phys Rev E 2022; 106:034135. [PMID: 36266866 DOI: 10.1103/physreve.106.034135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
We introduce heat engines working in the nanoregime that allow one to extract a finite amount of deterministic work. Using the resource theory approach to themodynamics, we show that the efficiency of these cycles is strictly smaller than Carnot's, and we associate this difference with a fundamental irreversibility that is present in single-shot transformations. When fluctuations in the extracted work are allowed there is a trade-off between their size and the efficiency. As the size of fluctuations increases so does the efficiency and optimal efficiency is attained for unbounded fluctuations, while a certain amount of deterministic work is drawn from the cycle. Finally, we show that when the working medium is composed of many particles, by creating an amount of correlations between the subsystems that scale logarithmically with their number, Carnot's efficiency can also be approached in the asymptotic limit along with deterministic work extraction.
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Affiliation(s)
- Federico Cerisola
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
- Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
| | - Facundo Sapienza
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- Department of Statistics, University of California, Berkeley, 367 Evans Hall, Berkeley, California 94720, USA
| | - Augusto J Roncaglia
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
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7
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Mukherjee V, Divakaran U. Many-body quantum thermal machines. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:454001. [PMID: 34359061 DOI: 10.1088/1361-648x/ac1b60] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
Thermodynamics of quantum systems and quantum thermal machines are rapidly developing fields, which have already delivered several promising results, as well as raised many intriguing questions. Many-body quantum machines present new opportunities stemming from many-body effects. At the same time, they pose new challenges related to many-body physics. In this short review we discuss some of the recent developments on technologies based on many-body quantum systems. We mainly focus on many-body effects in quantum thermal machines. We also briefly address the role played by many-body systems in the development of quantum batteries and quantum probes.
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Affiliation(s)
- Victor Mukherjee
- Department of Physical Sciences, IISER Berhampur, Berhampur 760010, India
| | - Uma Divakaran
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad, 678557, India
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8
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Purves T, Short AJ. Channels, measurements, and postselection in quantum thermodynamics. Phys Rev E 2021; 104:014111. [PMID: 34412318 DOI: 10.1103/physreve.104.014111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 06/17/2021] [Indexed: 11/07/2022]
Abstract
We analyze the benefit, in terms of extracting work, of having a single use of a quantum channel or measurement in quantum thermodynamics. This highlights a connection between unital and catalytic channels, and some subtleties concerning the conditional work cost of implementing a measurement given that a certain result was obtained. We also consider postselected measurements and show that any nontrivial postselection leads to an unbounded work benefit.
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Affiliation(s)
- Tom Purves
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Anthony J Short
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
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9
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Currencies in Resource Theories. ENTROPY 2021; 23:e23060755. [PMID: 34204010 PMCID: PMC8233888 DOI: 10.3390/e23060755] [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: 04/12/2021] [Revised: 06/09/2021] [Accepted: 06/11/2021] [Indexed: 11/24/2022]
Abstract
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources.
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10
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Łobejko M. The tight Second Law inequality for coherent quantum systems and finite-size heat baths. Nat Commun 2021; 12:918. [PMID: 33568672 PMCID: PMC7876128 DOI: 10.1038/s41467-021-21140-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/13/2021] [Indexed: 11/08/2022] Open
Abstract
In classical thermodynamics, the optimal work is given by the free energy difference, what according to the result of Skrzypczyk et al. can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and ideal energy storage that is able to extract work from coherences. Here we present the tight Second Law inequality, defined in terms of the ergotropy (rather than free energy), that incorporates both of those important microscopic effects - the locked energy in coherences and the locked energy due to the finite-size bath. The former is solely quantified by the so-called control-marginal state, whereas the latter is given by the free energy difference between the global passive state and the equilibrium state. Furthermore, we discuss the thermodynamic limit where the finite-size bath correction vanishes, and the locked energy in coherences takes the form of the entropy difference. We supplement our results by numerical simulations for the heat bath given by the collection of qubits and the Gaussian model of the work reservoir.
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Affiliation(s)
- Marcin Łobejko
- Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland.
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11
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García-Pintos LP, Hamma A, Del Campo A. Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries. PHYSICAL REVIEW LETTERS 2020; 125:040601. [PMID: 32794781 DOI: 10.1103/physrevlett.125.040601] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a "free energy operator," defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.
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Affiliation(s)
- Luis Pedro García-Pintos
- Joint Center for Quantum Information and Computer Science and Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Alioscia Hamma
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
- Donostia International Physics Center, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
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12
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Still Minding the Gap? Reflecting on Transitions between Concepts of Information in Varied Domains. INFORMATION 2020. [DOI: 10.3390/info11020071] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
This conceptual paper, a contribution to the tenth anniversary Special Issue of Information, gives a cross-disciplinary review of general and unified theories of information. A selective literature review is used to update a 2013 article on bridging the gaps between conceptions of information in different domains, including material from the physical and biological sciences, from the humanities and social sciences including library and information science, and from philosophy. A variety of approaches and theories are reviewed, including those of Brenner, Brier, Burgin and Wu, Capurro, Cárdenas-García and Ireland, Hidalgo, Hofkirchner, Kolchinsky and Wolpert, Floridi, Mingers and Standing, Popper, and Stonier. The gaps between disciplinary views of information remain, although there has been progress, and increasing interest, in bridging them. The solution is likely to be either a general theory of sufficient flexibility to cope with multiple meanings of information, or multiple and distinct theories for different domains, but with a complementary nature, and ideally boundary spanning concepts.
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13
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Beyer K, Luoma K, Strunz WT. Steering Heat Engines: A Truly Quantum Maxwell Demon. PHYSICAL REVIEW LETTERS 2019; 123:250606. [PMID: 31922791 DOI: 10.1103/physrevlett.123.250606] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 07/15/2019] [Indexed: 06/10/2023]
Abstract
We address the question of verifying the quantumness of thermal machines. A Szilárd engine is truly quantum if its work output cannot be described by a local hidden state model, i.e., an objective local statistical ensemble. Quantumness in this scenario is revealed by a steering-type inequality which bounds the classically extractable work. A quantum Maxwell demon can violate that inequality by exploiting quantum correlations between the work medium and the thermal environment. While for a classical Szilárd engine an objective description of the medium always exists, any such description can be ruled out by a steering task in a truly quantum case.
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Affiliation(s)
- Konstantin Beyer
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
| | - Kimmo Luoma
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
| | - Walter T Strunz
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062, Dresden, Germany
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14
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Clivaz F, Silva R, Haack G, Brask JB, Brunner N, Huber M. Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs. Phys Rev E 2019; 100:042130. [PMID: 31770926 DOI: 10.1103/physreve.100.042130] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Indexed: 11/07/2022]
Abstract
In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.
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Affiliation(s)
- Fabien Clivaz
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.,Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
| | - Ralph Silva
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Géraldine Haack
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Jonatan Bohr Brask
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.,Department of Physics, Technical University of Denmark, Fysikvej, Kongens Lyngby 2800, Denmark
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Marcus Huber
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
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15
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Lostaglio M. An introductory review of the resource theory approach to thermodynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:114001. [PMID: 31546240 DOI: 10.1088/1361-6633/ab46e5] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics covered include the so-called 'many second laws of thermodynamics', thermo-majorisation and symmetry constraints on the evolution of quantum coherence. Among the elementary applications, I explicitly work out the bounds on deterministic work extraction and formation, discuss the complete solution of the theory for a single qubit and present the irreversibility of coherence transfers. The aim is to facilitate the task of those researchers interested in engaging and contributing to this topic, presenting scope and motivation of its core assumptions and discussing the relation between the resource theory and complementary approaches.
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Affiliation(s)
- Matteo Lostaglio
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain
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16
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Clivaz F, Silva R, Haack G, Brask JB, Brunner N, Huber M. Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling. PHYSICAL REVIEW LETTERS 2019; 123:170605. [PMID: 31702237 DOI: 10.1103/physrevlett.123.170605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Revised: 09/24/2019] [Indexed: 06/10/2023]
Abstract
Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this Letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.
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Affiliation(s)
- Fabien Clivaz
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
| | - Ralph Silva
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Géraldine Haack
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Jonatan Bohr Brask
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
- Department of Physics, Technical University of Denmark, Fysikvej, Kongens Lyngby 2800, Denmark
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
| | - Marcus Huber
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
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17
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Shastry A, Xu Y, Stafford CA. The third law of thermodynamics in open quantum systems. J Chem Phys 2019. [DOI: 10.1063/1.5100182] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Abhay Shastry
- Department of Physics, University of Arizona, 1118 East Fourth Street, Tucson, Arizona 85721, USA
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H4, Canada
| | - Yiheng Xu
- Department of Physics, University of Arizona, 1118 East Fourth Street, Tucson, Arizona 85721, USA
- Department of Physics, University of California, San Diego, California 92093, USA
| | - Charles A. Stafford
- Department of Physics, University of Arizona, 1118 East Fourth Street, Tucson, Arizona 85721, USA
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18
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Raeisi S, Kieferová M, Mosca M. Novel Technique for Robust Optimal Algorithmic Cooling. PHYSICAL REVIEW LETTERS 2019; 122:220501. [PMID: 31283276 DOI: 10.1103/physrevlett.122.220501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Indexed: 06/09/2023]
Abstract
Heat-bath algorithmic cooling provides algorithmic ways to improve the purity of quantum states. These techniques are complex iterative processes that change from each iteration to the next and this poses a significant challenge to implementing these algorithms. Here, we introduce a new technique that on a fundamental level, shows that it is possible to do algorithmic cooling and even reach the cooling limit without any knowledge of the state and using only a single fixed operation, and on a practical level, presents a more feasible and robust alternative for implementing heat-bath algorithmic cooling. We also show that our new technique converges to the asymptotic state of heat-bath algorithmic cooling and that the cooling algorithm can be efficiently implemented; however, the saturation could require exponentially many iterations and remains impractical. This brings heat-bath algorithmic cooling to the realm of feasibility and makes it a viable option for realistic application in quantum technologies.
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Affiliation(s)
- Sadegh Raeisi
- Department of Physics, Sharif University of Technology, Tehran 1458889694, Iran
| | - Mária Kieferová
- Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, Macquarie University, Sydney, New South Wales 2109, Australia
| | - Michele Mosca
- Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1, Canada
- Department of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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19
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Abstract
The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost. Correlations in quantum thermodynamics are usually regarded as a useful but expensive resource. Here, the authors prove that the work cost of generating multiple copies of a state is lower if the copies are correlated, pointing out at the irreversibility of the process in the single-shot regime.
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Boes P, Eisert J, Gallego R, Müller MP, Wilming H. Von Neumann Entropy from Unitarity. PHYSICAL REVIEW LETTERS 2019; 122:210402. [PMID: 31283324 DOI: 10.1103/physrevlett.122.210402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Revised: 03/26/2019] [Indexed: 06/09/2023]
Abstract
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state when many identical and independent (i.i.d.) copies of the state are available, in a regime that is often referred to as being asymptotic. In this Letter, we provide a new operational characterization of the von Neumann entropy which neither requires an i.i.d. limit nor any explicit randomness. We do so by showing that the von Neumann entropy fully characterizes single-shot state transitions in unitary quantum mechanics, as long as one has access to a catalyst-an ancillary system that can be reused after the transition-and an environment which has the effect of dephasing in a preferred basis. Building upon these insights, we formulate and provide evidence for the catalytic entropy conjecture, which states that the above result holds true even in the absence of decoherence. If true, this would prove an intimate connection between single-shot state transitions in unitary quantum mechanics and the von Neumann entropy. Our results add significant support to recent insights that, contrary to common wisdom, the standard von Neumann entropy also characterizes single-shot situations and opens up the possibility for operational single-shot interpretations of other standard entropic quantities. We discuss implications of these insights to readings of the third law of quantum thermodynamics and hint at potentially profound implications to holography.
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Affiliation(s)
- Paul Boes
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Jens Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Rodrigo Gallego
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Markus P Müller
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Henrik Wilming
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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Richens JG, Alhambra ÁM, Masanes L. Finite-bath corrections to the second law of thermodynamics. Phys Rev E 2018; 97:062132. [PMID: 30011472 DOI: 10.1103/physreve.97.062132] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Indexed: 11/06/2022]
Abstract
The second law of thermodynamics states that a system in contact with a heat bath can undergo a transformation if and only if its free energy decreases. However, the "if" part of this statement is only true when the effective heat bath is infinite. In this article we remove this idealization and derive corrections to the second law in the case where the bath has a finite size, or equivalently finite heat capacity. This can also be translated to processes lasting a finite time, and we show that thermodynamical reversibility is lost in this regime. We do so in full generality, without assuming any particular model for the bath; the only parameters defining the bath are its temperature and heat capacity. We find connections with second order Shannon information theory, in particular, in the case of Landauer erasure. We also consider the case of nonfluctuating work and derive finite-bath corrections to the min and max free energies employed in single-shot thermodynamics.
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Affiliation(s)
- Jonathan G Richens
- Controlled Quantum Dynamics Theory Group, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.,Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Álvaro M Alhambra
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Lluis Masanes
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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22
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Miller HJD, Anders J. Energy-temperature uncertainty relation in quantum thermodynamics. Nat Commun 2018; 9:2203. [PMID: 29875440 PMCID: PMC5989247 DOI: 10.1038/s41467-018-04536-7] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 05/08/2018] [Indexed: 11/09/2022] Open
Abstract
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. However, for nanoscale systems deviations from standard thermodynamics arise due to their interactions with the environment. Here we include such interactions and, using quantum estimation theory, derive a generalised thermodynamic uncertainty relation valid for classical and quantum systems at all coupling strengths. We show that the non-commutativity between the system's state and its effective energy operator gives rise to quantum fluctuations that increase the temperature uncertainty. Surprisingly, these additional fluctuations are described by the average Wigner-Yanase-Dyson skew information. We demonstrate that the temperature's signal-to-noise ratio is constrained by the heat capacity plus a dissipative term arising from the non-negligible interactions. These findings shed light on the interplay between classical and non-classical fluctuations in quantum thermodynamics and will inform the design of optimal nanoscale thermometers.
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Affiliation(s)
- H J D Miller
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
| | - J Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
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Attraction Controls the Entropy of Fluctuations in Isosceles Triangular Networks. ENTROPY 2018; 20:e20020122. [PMID: 33265213 PMCID: PMC7512615 DOI: 10.3390/e20020122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Revised: 02/08/2018] [Accepted: 02/10/2018] [Indexed: 11/16/2022]
Abstract
We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system.
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Abstract
In most studies for the quantification of the third law of thermodynamics, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator to show that the minimum temperature which can be obtained in this system scales exponentially with the available time. The present work is expected to motivate further research in the active quest for absolute zero.
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Affiliation(s)
- Dionisis Stefanatos
- Division of Physical Sciences and Applications, Hellenic Army Academy, Vari, Athens 16673, Greece
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25
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Introduction to Quantum Thermodynamics: History and Prospects. FUNDAMENTAL THEORIES OF PHYSICS 2018. [DOI: 10.1007/978-3-319-99046-0_1] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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26
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Ito K, Hayashi M. Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling. Phys Rev E 2018; 97:012129. [PMID: 29448373 DOI: 10.1103/physreve.97.012129] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Indexed: 06/08/2023]
Abstract
In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.
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Affiliation(s)
- Kosuke Ito
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
| | - Masahito Hayashi
- Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
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28
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Richens JG, Masanes L. Work extraction from quantum systems with bounded fluctuations in work. Nat Commun 2016; 7:13511. [PMID: 27886177 PMCID: PMC5133619 DOI: 10.1038/ncomms13511] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Accepted: 10/07/2016] [Indexed: 11/20/2022] Open
Abstract
In the standard framework of thermodynamics, work is a random variable whose average is bounded by the change in free energy of the system. This average work is calculated without regard for the size of its fluctuations. Here we show that for some processes, such as reversible cooling, the fluctuations in work diverge. Realistic thermal machines may be unable to cope with arbitrarily large fluctuations. Hence, it is important to understand how thermodynamic efficiency rates are modified by bounding fluctuations. We quantify the work content and work of formation of arbitrary finite dimensional quantum states when the fluctuations in work are bounded by a given amount c. By varying c we interpolate between the standard and minimum free energies. We derive fundamental trade-offs between the magnitude of work and its fluctuations. As one application of these results, we derive the corrected Carnot efficiency of a qubit heat engine with bounded fluctuations.
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Affiliation(s)
- Jonathan G. Richens
- Controlled Quantum Dynamics Theory Group, Department of Physics, Imperial College London, London SW7 2AZ, UK
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
| | - Lluis Masanes
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
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