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Cerisola F, Mayo F, Roncaglia AJ. A Wigner Quasiprobability Distribution of Work. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1439. [PMID: 37895560 PMCID: PMC10606729 DOI: 10.3390/e25101439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Revised: 10/06/2023] [Accepted: 10/08/2023] [Indexed: 10/29/2023]
Abstract
In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition that can be directly measured in a real experiment. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of features related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution, it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences.
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Affiliation(s)
- Federico Cerisola
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - Franco Mayo
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
| | - Augusto J. Roncaglia
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; (F.M.); (A.J.R.)
- Instituto de Física de Buenos Aires (IFIBA), CONICET—Universidad de Buenos Aires, Buenos Aires C1121A6B, Argentina
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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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Korzekwa K, Lostaglio M. Optimizing Thermalization. PHYSICAL REVIEW LETTERS 2022; 129:040602. [PMID: 35939010 DOI: 10.1103/physrevlett.129.040602] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 04/27/2022] [Indexed: 06/15/2023]
Abstract
We present a rigorous approach, based on the concept of continuous thermomajorization, to algorithmically characterize the full set of energy occupations of a quantum system accessible from a given initial state through weak interactions with a heat bath. The algorithm can be deployed to solve complex optimization problems in out-of-equilibrium setups and it returns explicit elementary control sequences realizing optimal transformations. We illustrate this by finding optimal protocols in the context of cooling, work extraction, and catalysis. The same tools also allow one to quantitatively assess the role played by memory effects in the performance of thermodynamic protocols. We obtained exhaustive solutions on a laptop machine for systems with dimension d≤7, but with heuristic methods one could access much higher d.
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Affiliation(s)
- Kamil Korzekwa
- Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland
| | - Matteo Lostaglio
- Korteweg-de Vries Institute for Mathematics and QuSoft, University of Amsterdam, Science Park 105-107, 1098 XG Amsterdam, Netherlands
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
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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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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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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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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: 24] [Impact Index Per Article: 4.8] [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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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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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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Perarnau-Llobet M, Bäumer E, Hovhannisyan KV, Huber M, Acin A. No-Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems. PHYSICAL REVIEW LETTERS 2017; 118:070601. [PMID: 28256888 DOI: 10.1103/physrevlett.118.070601] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Indexed: 06/06/2023]
Abstract
An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement both at the beginning and at the end of the process, the first measurement destroys any initial coherence in the energy basis. Here we seek extensions of this approach which can possibly account for initially coherent states. We consider all measurement schemes to estimate work and require that (i) the difference of average energy corresponds to average work for closed quantum systems and that (ii) the work statistics agree with the standard two-measurement scheme for states with no coherence in the energy basis. We first show that such a scheme cannot exist. Next, we consider the possibility of performing collective measurements on several copies of the state and prove that it is still impossible to simultaneously satisfy requirements (i) and (ii). Nevertheless, improvements do appear, and in particular, we develop a measurement scheme that acts simultaneously on two copies of the state and allows us to describe a whole class of coherent transformations.
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Affiliation(s)
- Martí Perarnau-Llobet
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Elisa Bäumer
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Karen V Hovhannisyan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Marcus Huber
- Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
| | - Antonio Acin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
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