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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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2
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Kolchinsky A, Wolpert DH. Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes. Phys Rev E 2021; 104:054107. [PMID: 34942730 DOI: 10.1103/physreve.104.054107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 09/28/2021] [Indexed: 11/07/2022]
Abstract
We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state ρ, above the minimum EP incurred by the same process on any initial state. We show that this additional EP, which we term the "mismatch cost of ρ," has a universal information-theoretic form: it is given by the contraction of the relative entropy between ρ and the least-dissipative initial state φ over time. We derive versions of this result for integrated EP incurred over the course of a process, for trajectory-level fluctuating EP, and for instantaneous EP rate. We also show that mismatch cost for fluctuating EP obeys an integral fluctuation theorem. Our results demonstrate a fundamental relationship between thermodynamic irreversibility (generation of EP) and logical irreversibility (inability to know the initial state corresponding to a given final state). We use this relationship to derive quantitative bounds on the thermodynamics of quantum error correction and to propose a thermodynamically operationalized measure of the logical irreversibility of a quantum channel. Our results hold for both finite- and infinite-dimensional systems, and generalize beyond EP to many other thermodynamic costs, including nonadiabatic EP, free-energy loss, and entropy gain.
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Affiliation(s)
- Artemy Kolchinsky
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
| | - David H Wolpert
- Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
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3
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Kolchinsky A, Wolpert DH. Entropy production given constraints on the energy functions. Phys Rev E 2021; 104:034129. [PMID: 34654169 DOI: 10.1103/physreve.104.034129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/25/2021] [Indexed: 11/07/2022]
Abstract
We consider the problem of driving a finite-state classical system from some initial distribution p to some final distribution p^{'} with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in {p,p^{'}} and a graph-theoretic property defined in terms of E. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation p→p^{'} can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.
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Kwon H, Jeong H, Jennings D, Yadin B, Kim MS. Clock-Work Trade-Off Relation for Coherence in Quantum Thermodynamics. PHYSICAL REVIEW LETTERS 2018; 120:150602. [PMID: 29756899 DOI: 10.1103/physrevlett.120.150602] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Revised: 02/07/2018] [Indexed: 06/08/2023]
Abstract
In thermodynamics, quantum coherences-superpositions between energy eigenstates-behave in distinctly nonclassical ways. Here we describe how thermodynamic coherence splits into two kinds-"internal" coherence that admits an energetic value in terms of thermodynamic work, and "external" coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence, we provide dynamical constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clock-work trade-off relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system.
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Affiliation(s)
- Hyukjoon Kwon
- Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
| | - Hyunseok Jeong
- Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
| | - David Jennings
- Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Benjamin Yadin
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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Perarnau-Llobet M, Wilming H, Riera A, Gallego R, Eisert J. Strong Coupling Corrections in Quantum Thermodynamics. PHYSICAL REVIEW LETTERS 2018; 120:120602. [PMID: 29694098 DOI: 10.1103/physrevlett.120.120602] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2017] [Revised: 12/19/2017] [Indexed: 06/08/2023]
Abstract
Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic non-Markovian quantum Brownian motion.
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Affiliation(s)
- M Perarnau-Llobet
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - H Wilming
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - A Riera
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - R Gallego
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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6
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Lekscha J, Wilming H, Eisert J, Gallego R. Quantum thermodynamics with local control. Phys Rev E 2018; 97:022142. [PMID: 29548160 DOI: 10.1103/physreve.97.022142] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2017] [Indexed: 11/07/2022]
Abstract
We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to alternative bounds for the performance of engines. Our findings show that those limitations in control render it, in general, impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency or finite work per particle. We focus on the one-dimensional Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the antiferromagnetic case improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.
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Affiliation(s)
- J Lekscha
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.,Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.,Department of Physics, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - H Wilming
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - R Gallego
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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7
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Masanes L, Oppenheim J. A general derivation and quantification of the third law of thermodynamics. Nat Commun 2017; 8:14538. [PMID: 28290452 PMCID: PMC5355879 DOI: 10.1038/ncomms14538] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Accepted: 01/09/2017] [Indexed: 11/09/2022] Open
Abstract
The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased.
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Affiliation(s)
- Lluís Masanes
- Department of Physics & Astronomy, University College of London, London WC1E 6BT, UK
| | - Jonathan Oppenheim
- Department of Physics & Astronomy, University College of London, London WC1E 6BT, UK
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Friis N, Huber M, Perarnau-Llobet M. Energetics of correlations in interacting systems. Phys Rev E 2016; 93:042135. [PMID: 27176282 DOI: 10.1103/physreve.93.042135] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Indexed: 11/07/2022]
Abstract
A fundamental connection between thermodynamics and information theory arises from the fact that correlations exhibit an inherent work value. For noninteracting systems this translates to a work cost for establishing correlations. Here we investigate the relationship between work and correlations in the presence of interactions that cannot be controlled or removed. For such naturally coupled systems, which are correlated even in thermal equilibrium, we determine general strategies that can reduce the work cost of correlations, and illustrate these for a selection of exemplary physical systems.
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Affiliation(s)
- Nicolai Friis
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria
| | - Marcus Huber
- Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland.,Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain.,ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Martí Perarnau-Llobet
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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