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Céleri LC, Rudnicki Ł. Gauge-Invariant Quantum Thermodynamics: Consequences for the First Law. Entropy (Basel) 2024; 26:111. [PMID: 38392366 PMCID: PMC10888098 DOI: 10.3390/e26020111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Revised: 01/22/2024] [Accepted: 01/23/2024] [Indexed: 02/24/2024]
Abstract
The universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse graining, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry-essential in all modern physical theories-we put forward a new possible intermediate route. Working within the realm of quantum thermodynamics, we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse graining behind thermodynamics. As a first application of this new framework, we reinterpret quantum work and heat, as well as the role of quantum coherence.
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Affiliation(s)
- Lucas C Céleri
- QPequi Group, Institute of Physics, Federal University of Goiás, Goiânia 74690-900, Brazil
| | - Łukasz Rudnicki
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
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Arrais EG, Wisniacki DA, Céleri LC, de Almeida NG, Roncaglia AJ, Toscano F. Quantum work for sudden quenches in Gaussian random Hamiltonians. Phys Rev E 2018; 98:012106. [PMID: 30110827 DOI: 10.1103/physreve.98.012106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Indexed: 06/08/2023]
Abstract
In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state, and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function G(u), associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of G(u) calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.
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Affiliation(s)
- Eric G Arrais
- Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, Brazil
| | - Diego A Wisniacki
- Departamento de Física "J. J. Giambiagi" and IFIBA, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
| | - Lucas C Céleri
- Instituto de Física, Universidade Federal de Goiás, 74001-970 Goiânia, Brazil
| | - Norton G de Almeida
- Instituto de Física, Universidade Federal de Goiás, 74001-970 Goiânia, Brazil
| | - Augusto J Roncaglia
- Departamento de Física "J. J. Giambiagi" and IFIBA, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
| | - Fabricio Toscano
- Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, Brazil
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Peterson JPS, Sarthour RS, Souza AM, Oliveira IS, Goold J, Modi K, Soares-Pinto DO, Céleri LC. Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit. Proc Math Phys Eng Sci 2016; 472:20150813. [PMID: 27274690 DOI: 10.1098/rspa.2015.0813] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance set-up to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins [Formula: see text] (qubits) molecule-the system, the reservoir and the ancilla-to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique, we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way, we were able to verify that an operation that changes the information content of the system must necessarily generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.
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Affiliation(s)
- J P S Peterson
- Centro Brasileiro de Pesquisas Físicas , Rua Dr Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - R S Sarthour
- Centro Brasileiro de Pesquisas Físicas , Rua Dr Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - A M Souza
- Centro Brasileiro de Pesquisas Físicas , Rua Dr Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - I S Oliveira
- Centro Brasileiro de Pesquisas Físicas , Rua Dr Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - J Goold
- The Abdus Salam International Centre for Theoretical Physics (ICTP) , Trieste, Italy
| | - K Modi
- School of Physics and Astronomy, Monash University , Victoria 3800, Australia
| | - D O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo , CP 369, 13560-970, São Carlos, SP, Brazil
| | - L C Céleri
- Instituto de Física, Universidade Federal de Goiás , Caixa Postal 131 74001-970, Goiânia, Brazil
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Micadei K, Serra RM, Céleri LC. Thermodynamic cost of acquiring information. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:062123. [PMID: 24483402 DOI: 10.1103/physreve.88.062123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Indexed: 06/03/2023]
Abstract
Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information-assisted work extraction have greatly contributed not only to broadening our understanding about the fundamental limits imposed by nature, but also paving the way for practical implementations of information-processing devices. The intricate information-thermodynamics relation also entails a fundamental limit on parameter estimation, establishing a thermodynamic cost for information acquisition. We show that the amount of information that can be encoded in a physical system by means of a unitary process is limited by the dissipated work during the implementation of the process. This includes a thermodynamic tradeoff for information acquisition. Likewise, the information acquisition process is ultimately limited by the second law of thermodynamics. This tradeoff for information acquisition may find applications in several areas of knowledge.
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Affiliation(s)
- Kaonan Micadei
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André, São Paulo, Brazil
| | - Roberto M Serra
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, R. Santa Adélia 166, 09210-170 Santo André, São Paulo, Brazil
| | - Lucas C Céleri
- Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, Goiás, Brazil
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Soares-Pinto DO, Auccaise R, Maziero J, Gavini-Viana A, Serra RM, Céleri LC. On the quantumness of correlations in nuclear magnetic resonance. Philos Trans A Math Phys Eng Sci 2012; 370:4821-4836. [PMID: 22946043 DOI: 10.1098/rsta.2011.0364] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.
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Affiliation(s)
- D O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
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Auccaise R, Céleri LC, Soares-Pinto DO, deAzevedo ER, Maziero J, Souza AM, Bonagamba TJ, Sarthour RS, Oliveira IS, Serra RM. Environment-induced sudden transition in quantum discord dynamics. Phys Rev Lett 2011; 107:140403. [PMID: 22107179 DOI: 10.1103/physrevlett.107.140403] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2011] [Indexed: 05/31/2023]
Abstract
Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.
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Affiliation(s)
- R Auccaise
- Empresa Brasileira de Pesquisa Agropecuária, Rua Jardim Botânico 1024, 22460-000 Rio de Janeiro, Rio de Janeiro, Brazil
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Auccaise R, Maziero J, Céleri LC, Soares-Pinto DO, deAzevedo ER, Bonagamba TJ, Sarthour RS, Oliveira IS, Serra RM. Experimentally witnessing the quantumness of correlations. Phys Rev Lett 2011; 107:070501. [PMID: 21902378 DOI: 10.1103/physrevlett.107.070501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Indexed: 05/31/2023]
Abstract
The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.
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Affiliation(s)
- R Auccaise
- Empresa Brasileira de Pesquisa Agropecuária, Rio de Janeiro, Brazil
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