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Van Vu T, Saito K. Thermodynamics of Precision in Markovian Open Quantum Dynamics. PHYSICAL REVIEW LETTERS 2022; 128:140602. [PMID: 35476476 DOI: 10.1103/physrevlett.128.140602] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Revised: 03/02/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.
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Affiliation(s)
- Tan Van Vu
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
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Moslonka C, Sekimoto K. Martingale-induced local invariance in progressive quenching. Phys Rev E 2022; 105:044146. [PMID: 35590610 DOI: 10.1103/physreve.105.044146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 02/24/2022] [Indexed: 06/15/2023]
Abstract
Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that during PQ, the mean equilibrium spin value follows a martingale process and this process can characterize the memory of the system. In the present study, we find that the aforementioned martingale implies a local invariance of the path weight for the total quenched magnetization, the Markovian process whose increment is the spin that is fixed last. Consequently, PQ lets the probability distribution for the total quenched magnetization evolve while keeping the Boltzmann-like factor, or a canonical structure, under constraint, which consists of a path-independent potential and a path-counting entropy. Moreover, when the PQ starts from full equilibrium, the probability distribution at each stage of PQ is found to be the limit distribution of what we call recycled quenching, the process in which a randomly chosen quenched spin is unquenched after a single step of PQ. The local invariance is directly derived from the martingale property, and not from other known theorems on martingale processes.
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Affiliation(s)
- Charles Moslonka
- Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL 10 rue Vauquelin, 75005 Paris, France
| | - Ken Sekimoto
- Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL 10 rue Vauquelin, 75005 Paris, France
- Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université de Paris, 10 Rue Alice Domon et Léonie Duquet, 75013 Paris, France
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Manzano G, Roldán É. Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines. Phys Rev E 2022; 105:024112. [PMID: 35291142 DOI: 10.1103/physreve.105.024112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities do not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in nonequilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.
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Affiliation(s)
- Gonzalo Manzano
- Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
- Institute for Quantum Optics and Quantum Information IQOQI, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Édgar Roldán
- ICTP-Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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Van Vu T, Hasegawa Y. Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2021; 127:190601. [PMID: 34797124 DOI: 10.1103/physrevlett.127.190601] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 10/04/2021] [Indexed: 06/13/2023]
Abstract
We consider the thermal relaxation process of a quantum system attached to single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower bounded by a relative entropy between the unitarily evolved state and the final state. The bound characterizes the state discrepancy induced by the nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.
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Affiliation(s)
- Tan Van Vu
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
| | - Yoshihiko Hasegawa
- Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan
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Manzano G, Subero D, Maillet O, Fazio R, Pekola JP, Roldán É. Thermodynamics of Gambling Demons. PHYSICAL REVIEW LETTERS 2021; 126:080603. [PMID: 33709732 DOI: 10.1103/physrevlett.126.080603] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 11/23/2020] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum nonstationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.
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Affiliation(s)
- Gonzalo Manzano
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Diego Subero
- PICO group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Olivier Maillet
- PICO group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Rosario Fazio
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Dipartimento di Fisica, Università di Napoli "Federico II," Monte S. Angelo, I-80126 Napoli, Italy
| | - Jukka P Pekola
- PICO group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Édgar Roldán
- International Centre for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
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Nation C, Porras D. Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories. Phys Rev E 2020; 102:042115. [PMID: 33212596 DOI: 10.1103/physreve.102.042115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 09/12/2020] [Indexed: 06/11/2023]
Abstract
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.
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Affiliation(s)
- Charlie Nation
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
| | - Diego Porras
- Institute of Fundamental Physics, CSIC, Calle Serrano 113b, 28006 Madrid, Spain
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Neri I. Second Law of Thermodynamics at Stopping Times. PHYSICAL REVIEW LETTERS 2020; 124:040601. [PMID: 32058768 DOI: 10.1103/physrevlett.124.040601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Indexed: 06/10/2023]
Abstract
Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle when it escapes a metastable state. We develop a thermodynamic theory for processes in mesoscopic systems that terminate at stopping times, which generalize first-passage times. This theory implies a thermodynamic bound, reminiscent of the second law of thermodynamics, for the work exerted by an external protocol on a mesoscopic system at a stopping time. As an illustration, we use this law to bound the work required to stretch a polymer to a certain length or to let a particle escape from a metastable state.
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Affiliation(s)
- Izaak Neri
- Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
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Roldán É, Vivo P. Exact distributions of currents and frenesy for Markov bridges. Phys Rev E 2019; 100:042108. [PMID: 31770868 DOI: 10.1103/physreve.100.042108] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2019] [Indexed: 02/01/2023]
Abstract
We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to time-integrated currents and frenesy of enzymatic reactions, which may include absolutely irreversible transitions. We discuss the information that frenesy carries about the currents and show that bridges may violate known uncertainty relations in certain cases. Numerical simulations are in perfect agreement with our theory.
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Affiliation(s)
- Édgar Roldán
- ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Pierpaolo Vivo
- Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
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