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Murthy C, Babakhani A, Iniguez F, Srednicki M, Yunger Halpern N. Non-Abelian Eigenstate Thermalization Hypothesis. PHYSICAL REVIEW LETTERS 2023; 130:140402. [PMID: 37084457 DOI: 10.1103/physrevlett.130.140402] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Revised: 10/16/2022] [Accepted: 02/24/2023] [Indexed: 05/03/2023]
Abstract
The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector-in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.
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Affiliation(s)
- Chaitanya Murthy
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Arman Babakhani
- Department of Physics, University of Southern California, Los Angeles, California 90089, USA
- Information Sciences Institute, Marina Del Rey, California 90292, USA
| | - Fernando Iniguez
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Mark Srednicki
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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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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Yunger Halpern N, Beverland ME, Kalev A. Noncommuting conserved charges in quantum many-body thermalization. Phys Rev E 2020; 101:042117. [PMID: 32422760 DOI: 10.1103/physreve.101.042117] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2019] [Accepted: 03/17/2020] [Indexed: 11/07/2022]
Abstract
In statistical mechanics, a small system exchanges conserved quantities-heat, particles, electric charge, etc.-with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
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Affiliation(s)
- Nicole Yunger Halpern
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.,ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.,Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | - Amir Kalev
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742-2420, USA
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Mohammady MH, Romito A. Efficiency of a cyclic quantum heat engine with finite-size baths. Phys Rev E 2019; 100:012122. [PMID: 31499920 DOI: 10.1103/physreve.100.012122] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Indexed: 11/07/2022]
Abstract
In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.
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Affiliation(s)
- M Hamed Mohammady
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom.,RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia
| | - Alessandro Romito
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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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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Sparaciari C, Jennings D, Oppenheim J. Energetic instability of passive states in thermodynamics. Nat Commun 2017; 8:1895. [PMID: 29196705 PMCID: PMC5711874 DOI: 10.1038/s41467-017-01505-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Accepted: 09/22/2017] [Indexed: 11/16/2022] Open
Abstract
Passivity is a fundamental concept in thermodynamics that demands a quantum system's energy cannot be lowered by any reversible, unitary process acting on the system. In the limit of many such systems, passivity leads in turn to the concept of complete passivity, thermal states and the emergence of a thermodynamic temperature. Here we only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. Indeed, we show that given a single copy of any athermal quantum state, an optimal amount of energy can be extracted from it when we utilise a machine that operates in a reversible cycle. This means that for individual systems, the only form of passivity that is stable under general reversible processes is complete passivity, and thus provides a physically motivated identification of thermal states when we are not operating in the thermodynamic limit.
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Affiliation(s)
- Carlo Sparaciari
- Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK.
| | - David Jennings
- Department of Physics, University of Oxford, Oxford, OX1 3PU, UK.
- Department of Physics, Imperial College London, London, SW7 2AZ, UK.
| | - Jonathan Oppenheim
- Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK.
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