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Mixing indistinguishable systems leads to a quantum Gibbs paradox. Nat Commun 2021; 12:1471. [PMID: 33674586 PMCID: PMC7935879 DOI: 10.1038/s41467-021-21620-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 01/27/2021] [Indexed: 11/08/2022] Open
Abstract
The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an "ignorant" observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.
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Holmes Z, Anders J, Mintert F. Enhanced Energy Transfer to an Optomechanical Piston from Indistinguishable Photons. PHYSICAL REVIEW LETTERS 2020; 124:210601. [PMID: 32530653 DOI: 10.1103/physrevlett.124.210601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Revised: 03/24/2020] [Accepted: 04/30/2020] [Indexed: 06/11/2023]
Abstract
Thought experiments involving gases and pistons, such as Maxwell's demon and Gibbs' mixing, are central to our understanding of thermodynamics. Here, we present a quantum thermodynamic thought experiment in which the energy transfer from two photonic gases to a piston membrane grows quadratically with the number of photons for indistinguishable gases, while it grows linearly for distinguishable gases. This signature of bosonic bunching may be observed in optomechanical experiments, highlighting the potential of these systems for the realization of thermodynamic thought experiments in the quantum realm.
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Affiliation(s)
- Zoë Holmes
- Controlled Quantum Dynamics Theory Group, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
| | - Janet Anders
- Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
- Institut für Physik, Potsdam University, 14476 Potsdam, Germany
| | - Florian Mintert
- Controlled Quantum Dynamics Theory Group, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
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Landauer's Principle in a Quantum Szilard Engine without Maxwell's Demon. ENTROPY 2020; 22:e22030294. [PMID: 33286068 PMCID: PMC7516751 DOI: 10.3390/e22030294] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Revised: 02/28/2020] [Accepted: 03/01/2020] [Indexed: 11/27/2022]
Abstract
Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell’s Demon where Landauer’s principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell’s demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but the erasure and related heat dissipation still take place implicitly. We explore a quantum Szilard engine considering quantum size effects. We see that insertion of the partition does not localize the particle to one side, instead creating a superposition state of the particle being in both sides. To be able to extract work from the system, particle has to be localized at one side. The localization occurs as a result of quantum measurement on the particle, which shows the importance of the measurement process regardless of whether one uses the acquired information or not. In accordance with Landauer’s principle, localization by quantum measurement corresponds to a logically irreversible operation and for this reason it must be accompanied by the corresponding heat dissipation. This shows the validity of Landauer’s principle even in quantum Szilard engines without Maxwell’s demon.
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Myers NM, Deffner S. Bosons outperform fermions: The thermodynamic advantage of symmetry. Phys Rev E 2020; 101:012110. [PMID: 32069543 DOI: 10.1103/physreve.101.012110] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Indexed: 06/10/2023]
Abstract
We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that the bosonic system displays enhanced performance when compared to two independent single particle engines, while the fermionic system displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.
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Affiliation(s)
- Nathan M Myers
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
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Bengtsson J, Tengstrand MN, Wacker A, Samuelsson P, Ueda M, Linke H, Reimann SM. Quantum Szilard Engine with Attractively Interacting Bosons. PHYSICAL REVIEW LETTERS 2018; 120:100601. [PMID: 29570332 DOI: 10.1103/physrevlett.120.100601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Indexed: 06/08/2023]
Abstract
We show that a quantum Szilard engine containing many bosons with attractive interactions enhances the conversion between information and work. Using an ab initio approach to the full quantum-mechanical many-body problem, we find that the average work output increases significantly for a larger number of bosons. The highest overshoot occurs at a finite temperature, demonstrating how thermal and quantum effects conspire to enhance the conversion between information and work. The predicted effects occur over a broad range of interaction strengths and temperatures.
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Affiliation(s)
- J Bengtsson
- Mathematical Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | | | - A Wacker
- Mathematical Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - P Samuelsson
- Mathematical Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - M Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 11 3-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - H Linke
- Solid State Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
| | - S M Reimann
- Mathematical Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden
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Camati PA, Peterson JPS, Batalhão TB, Micadei K, Souza AM, Sarthour RS, Oliveira IS, Serra RM. Experimental Rectification of Entropy Production by Maxwell's Demon in a Quantum System. PHYSICAL REVIEW LETTERS 2016; 117:240502. [PMID: 28009191 DOI: 10.1103/physrevlett.117.240502] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Indexed: 06/06/2023]
Abstract
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
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Affiliation(s)
- Patrice A Camati
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - John P S Peterson
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Tiago B Batalhão
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Kaonan Micadei
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Alexandre M Souza
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Roberto S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Ivan S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - Roberto M Serra
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
- Department of Physics, University of York, York YO10 5DD, United Kingdom
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Vidrighin MD, Dahlsten O, Barbieri M, Kim MS, Vedral V, Walmsley IA. Photonic Maxwell's Demon. PHYSICAL REVIEW LETTERS 2016; 116:050401. [PMID: 26894692 DOI: 10.1103/physrevlett.116.050401] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Indexed: 06/05/2023]
Abstract
We report an experimental realization of Maxwell's demon in a photonic setup. We show that a measurement at the few-photons level followed by a feed-forward operation allows the extraction of work from intense thermal light into an electric circuit. The interpretation of the experiment stimulates the derivation of an equality relating work extraction to information acquired by measurement. We derive a bound using this relation and show that it is in agreement with the experimental results. Our work puts forward photonic systems as a platform for experiments related to information in thermodynamics.
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Affiliation(s)
- Mihai D Vidrighin
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Oscar Dahlsten
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- London Institute for Mathematical Sciences, 35a South Street, Mayfair WIK 2XF, United Kingdom
| | - Marco Barbieri
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, United Kingdom
| | - Vlatko Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Republic of Singapore
| | - Ian A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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