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Alvim YJ, Céleri LC. Landauer Principle and the Second Law in a Relativistic Communication Scenario. ENTROPY (BASEL, SWITZERLAND) 2024; 26:613. [PMID: 39056975 PMCID: PMC11276077 DOI: 10.3390/e26070613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2024] [Revised: 07/19/2024] [Accepted: 07/19/2024] [Indexed: 07/28/2024]
Abstract
The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical nature of information, which underpins Landauer's principle, we believe that information theory should play a role in understanding this problem. In this work, we contribute to this endeavour by considering a relativistic communication task between two partners, Alice and Bob, in a general Lorentzian spacetime. We then assume that the receiver, Bob, reversibly operates a local heat engine powered by information, and seek to determine the maximum amount of work he can extract from this device. As Bob cannot extract work for free, by applying both Landauer's principle and the second law of thermodynamics, we establish a bound on the energy Bob must spend to acquire the information in the first place. This bound is a function of the spacetime metric and the properties of the communication channel.
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Affiliation(s)
| | - Lucas C. Céleri
- QPequi Group, Institute of Physics, Federal University of Goiás, Goiânia 74690-900, Goiás, Brazil
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2
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Bormashenko E. Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives. ENTROPY (BASEL, SWITZERLAND) 2024; 26:423. [PMID: 38785672 PMCID: PMC11119825 DOI: 10.3390/e26050423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2024] [Revised: 04/25/2024] [Accepted: 05/14/2024] [Indexed: 05/25/2024]
Abstract
The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surroundings. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin, and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler's "it from bit" paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering.
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Affiliation(s)
- Edward Bormashenko
- Department of Chemical Engineering, Biotechnology and Materials, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel
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Croucher T, Vaccaro JA. Thermodynamics of memory erasure via a spin reservoir. Phys Rev E 2021; 103:042140. [PMID: 34006013 DOI: 10.1103/physreve.103.042140] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
Thermodynamics with multiple conserved quantities offers a promising direction for designing novel devices. For example, Vaccaro and Barnett's [J. A. Vaccaro and S. M. Barnett, Proc. R. Soc. A 467, 1770 (2011)1364-502110.1098/rspa.2010.0577; S. M. Barnett and J. A. Vaccaro, Entropy 15, 4956 (2013)ENTRFG1099-430010.3390/e15114956] proposed information erasure scheme, where the cost of erasure is solely in terms of a conserved quantity other than energy, allows for new kinds of heat engines. In recent work, we studied the discrete fluctuations and average bounds of the erasure cost in spin angular momentum. Here we clarify the costs in terms of the spin equivalent of work, called spinlabor, and the spin equivalent of heat, called spintherm. We show that the previously found bound on the erasure cost of γ^{-1}ln2 can be violated by the spinlabor cost, and only applies to the spintherm cost. We obtain three bounds for spinlabor for different erasure protocols and determine the one that provides the tightest bound. For completeness, we derive a generalized Jarzynski equality and probability of violation which shows that for particular protocols the probability of violation can be surprisingly large. We also derive an integral fluctuation theorem and use it to analyze the cost of information erasure using a spin reservoir.
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Affiliation(s)
- T Croucher
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - J A Vaccaro
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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Popescu S, Sainz AB, Short AJ, Winter A. Reference Frames Which Separately Store Noncommuting Conserved Quantities. PHYSICAL REVIEW LETTERS 2020; 125:090601. [PMID: 32915626 DOI: 10.1103/physrevlett.125.090601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2019] [Revised: 04/27/2020] [Accepted: 07/28/2020] [Indexed: 06/11/2023]
Abstract
Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a "battery" for a distinct quantity. For systems composed of spin-1/2 particles, we show that the components of angular momentum S_{x}, S_{y}, and S_{z} (noncommuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of noncommuting conserved quantities.
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Affiliation(s)
- Sandu Popescu
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Ana Belén Sainz
- International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
- Perimeter Institute for Theoretical Physics, Waterloo, N2L 2Y5 Ontario, Canada
| | - Anthony J Short
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Andreas Winter
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010 Barcelona, Spain
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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The Landauer Principle: Re-Formulation of the Second Thermodynamics Law or a Step to Great Unification? ENTROPY 2019. [PMCID: PMC7514250 DOI: 10.3390/e21100918] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The Landauer principle quantifies the thermodynamic cost of the recording/erasure of one bit of information, as it was stated by its author: “information is physical” and it has an energy equivalent. In its narrow sense, the Landauer principle states that the erasure of one bit of information requires a minimum energy cost equal to kBT ln2, where T is the temperature of a thermal reservoir used in the process and kB is Boltzmann’s constant. The Landauer principle remains highly debatable. It has been argued that, since it is not independent of the second law of thermodynamics, it is either unnecessary or insufficient as an exorcism of Maxwell’s demon. On the other hand, the Landauer principle enables the “informational” reformulation of thermodynamic laws. Thus, the Landauer principle touches the deepest physical roots of thermodynamics. Authors are invited to contribute papers devoted to the meaning, interpretation, physical roots, experimental verification and applications of the Landauer principle. Papers devoted to the quantum and relativity aspects of the Landauer principle are encouraged.
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Popescu S, Sainz AB, Short AJ, Winter A. Quantum reference frames and their applications to thermodynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2018.0111. [PMID: 29807906 PMCID: PMC5990656 DOI: 10.1098/rsta.2018.0111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/11/2018] [Indexed: 05/06/2023]
Abstract
We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
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Affiliation(s)
- Sandu Popescu
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
| | - Ana Belén Sainz
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Anthony J Short
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
| | - Andreas Winter
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys 23, 08010 Barcelona, Spain
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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Taranto P, Modi K, Pollock FA. Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes. Phys Rev E 2018; 97:052111. [PMID: 29906945 DOI: 10.1103/physreve.97.052111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Indexed: 06/08/2023]
Abstract
In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.
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Affiliation(s)
- Philip Taranto
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Kavan Modi
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Felix A Pollock
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
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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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Croucher T, Bedkihal S, Vaccaro JA. Discrete Fluctuations in Memory Erasure without Energy Cost. PHYSICAL REVIEW LETTERS 2017; 118:060602. [PMID: 28234546 DOI: 10.1103/physrevlett.118.060602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Indexed: 06/06/2023]
Abstract
According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.
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Affiliation(s)
- Toshio Croucher
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Salil Bedkihal
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Joan A Vaccaro
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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Weilenmann M, Kraemer L, Faist P, Renner R. Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies. PHYSICAL REVIEW LETTERS 2016; 117:260601. [PMID: 28059535 DOI: 10.1103/physrevlett.117.260601] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Indexed: 06/06/2023]
Abstract
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.
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Affiliation(s)
- Mirjam Weilenmann
- Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland
- Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom
| | - Lea Kraemer
- Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland
| | - Philippe Faist
- Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Renato Renner
- Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland
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Guryanova Y, Popescu S, Short AJ, Silva R, Skrzypczyk P. Thermodynamics of quantum systems with multiple conserved quantities. Nat Commun 2016; 7:12049. [PMID: 27384384 PMCID: PMC4941046 DOI: 10.1038/ncomms12049] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 05/23/2016] [Indexed: 11/08/2022] Open
Abstract
Recently, there has been much progress in understanding the thermodynamics of quantum systems, even for small individual systems. Most of this work has focused on the standard case where energy is the only conserved quantity. Here we consider a generalization of this work to deal with multiple conserved quantities. Each conserved quantity, which, importantly, need not commute with the rest, can be extracted and stored in its own battery. Unlike the standard case, in which the amount of extractable energy is constrained, here there is no limit on how much of any individual conserved quantity can be extracted. However, other conserved quantities must be supplied, and the second law constrains the combination of extractable quantities and the trade-offs between them. We present explicit protocols that allow us to perform arbitrarily good trade-offs and extract arbitrarily good combinations of conserved quantities from individual quantum systems.
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Affiliation(s)
- Yelena Guryanova
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Sandu Popescu
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Anthony J. Short
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Ralph Silva
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
- Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland
| | - Paul Skrzypczyk
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
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