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Saryal S, Mohanta S, Agarwalla BK. Bounds on fluctuations for machines with broken time-reversal symmetry: A linear response study. Phys Rev E 2022; 105:024129. [PMID: 35291179 DOI: 10.1103/physreve.105.024129] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator, or pump, is imposed on both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio between fluctuations of output and input current are obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relations for time-reversal symmetry-broken systems. We illustrate these findings for two different types of machines: (1) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field and (2) a periodically driven classical Brownian heat engine.
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Affiliation(s)
- Sushant Saryal
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Sandipan Mohanta
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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2
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Saryal S, Gerry M, Khait I, Segal D, Agarwalla BK. Universal Bounds on Fluctuations in Continuous Thermal Machines. PHYSICAL REVIEW LETTERS 2021; 127:190603. [PMID: 34797144 DOI: 10.1103/physrevlett.127.190603] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 06/07/2021] [Accepted: 09/27/2021] [Indexed: 06/13/2023]
Abstract
We study bounds on ratios of fluctuations in steady-state time-reversal energy conversion devices. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.
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Affiliation(s)
- Sushant Saryal
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Matthew Gerry
- Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Ilia Khait
- Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Dvira Segal
- Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6, Canada
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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3
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Jiao G, Zhu S, He J, Ma Y, Wang J. Fluctuations in irreversible quantum Otto engines. Phys Rev E 2021; 103:032130. [PMID: 33862833 DOI: 10.1103/physreve.103.032130] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 03/01/2021] [Indexed: 11/07/2022]
Abstract
We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.
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Affiliation(s)
- Guangqian Jiao
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Shoubao Zhu
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Yongli Ma
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China.,State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
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4
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Liu J, Segal D. Coherences and the thermodynamic uncertainty relation: Insights from quantum absorption refrigerators. Phys Rev E 2021; 103:032138. [PMID: 33862758 DOI: 10.1103/physreve.103.032138] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a tradeoff relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where nonzero coherence between eigenstates can either suppress or enhance the cooling power, compared with the incoherent limit. In either scenario, we find enhanced relative noise of the cooling power (standard deviation of the power over the mean) in the presence of system coherence, thereby corroborating the thermodynamic uncertainty relation. Our results indicate that fluctuations necessitate consideration when assessing the performance of quantum coherent thermal machines.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, M5S 3H6, Canada
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, M5S 3H6, Canada.,Department of Physics, 60 Saint George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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5
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Vroylandt H, Esposito M, Verley G. Efficiency Fluctuations of Stochastic Machines Undergoing a Phase Transition. PHYSICAL REVIEW LETTERS 2020; 124:250603. [PMID: 32639779 DOI: 10.1103/physrevlett.124.250603] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 05/13/2020] [Indexed: 06/11/2023]
Abstract
We study the efficiency fluctuations of a stochastic heat engine made of N interacting unicyclic machines and undergoing a phase transition in the macroscopic limit. Depending on N and on the observation time, the machine can explore its whole phase space or not. This affects the engine efficiency that either strongly fluctuates on a large interval of equiprobable efficiencies (ergodic case) or fluctuates close to several most likely values (nonergodic case). We also provide a proof that despite the phase transition, the decay rate of the efficiency distribution at the reversible efficiency remains largest one although other efficiencies can now decay equally fast.
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Affiliation(s)
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Material Science, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
| | - Gatien Verley
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
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6
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Liu F, Su S. Stochastic Floquet quantum heat engines and stochastic efficiencies. Phys Rev E 2020; 101:062144. [PMID: 32688492 DOI: 10.1103/physreve.101.062144] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
Based on the notion of quantum trajectory, we present a stochastic theoretical framework for Floquet quantum heat engines. As an application, the large deviation functions of two types of stochastic efficiencies for a two-level Floquet quantum heat engine are investigated. We find that the statistics of one efficiency agree well with the predictions of the universal theory of efficiency fluctuations developed by Verley et al. [Phys. Rev. E 90, 052145 (2014)10.1103/PhysRevE.90.052145], whereas the statistics of the other efficiency do not. The reason for this discrepancy is attributed to the lack of fluctuation theorems for the latter type of efficiency.
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Affiliation(s)
- Fei Liu
- School of Physics, Beihang University, Beijing 100191, China
| | - Shanhe Su
- Department of Physics, Xiamen University, Xiamen 361005, China
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7
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Liu Q, Li W, Zhang M, He J, Wang J. Efficiency Bounds for Minimally Nonlinear Irreversible Heat Engines with Broken Time-Reversal Symmetry. ENTROPY (BASEL, SWITZERLAND) 2019; 21:e21070717. [PMID: 33267431 PMCID: PMC7515233 DOI: 10.3390/e21070717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Revised: 07/12/2019] [Accepted: 07/17/2019] [Indexed: 06/12/2023]
Abstract
We study the minimally nonlinear irreversible heat engines in which the time-reversal symmetry for the systems may be broken. The expressions for the power and the efficiency are derived, in which the effects of the nonlinear terms due to dissipations are included. We show that, as within the linear responses, the minimally nonlinear irreversible heat engines can enable attainment of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn limit imposed on the efficiency at maximum power can be overcome if the time-reversal symmetry is broken.
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Affiliation(s)
- Qin Liu
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Wei Li
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Min Zhang
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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8
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Manikandan SK, Dabelow L, Eichhorn R, Krishnamurthy S. Efficiency Fluctuations in Microscopic Machines. PHYSICAL REVIEW LETTERS 2019; 122:140601. [PMID: 31050471 DOI: 10.1103/physrevlett.122.140601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Revised: 03/01/2019] [Indexed: 06/09/2023]
Abstract
Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a "universal theory of efficiency fluctuations" at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014)NCAOBW2041-172310.1038/ncomms5721; Phys. Rev. E 90, 052145 (2014)PRESCM1539-375510.1103/PhysRevE.90.052145]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the "universal features" and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.
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Affiliation(s)
| | - Lennart Dabelow
- Fakultät für Physik, Universität Bielefeld, 33615 Bielefeld, Germany
| | - Ralf Eichhorn
- Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
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Rosas A, Van den Broeck C, Lindenberg K. Stochastic thermodynamics for a periodically driven single-particle pump. Phys Rev E 2017; 96:052135. [PMID: 29347780 DOI: 10.1103/physreve.96.052135] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Indexed: 06/07/2023]
Abstract
We present the stochastic thermodynamic analysis of a time-periodic single-particle pump, including explicit results for flux, thermodynamic force, entropy production, work, heat, and efficiency. These results are valid far from equilibrium. The deviations from the linear (Onsager) regime are discussed.
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Affiliation(s)
- Alexandre Rosas
- Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900, João Pessoa, Brazil
| | | | - Katja Lindenberg
- Department of Chemistry and Biochemistry, and BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA
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10
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Proesmans K, Van den Broeck C. The underdamped Brownian duet and stochastic linear irreversible thermodynamics. CHAOS (WOODBURY, N.Y.) 2017; 27:104601. [PMID: 29092424 DOI: 10.1063/1.5001187] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.
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11
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Park JM, Chun HM, Noh JD. Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model. Phys Rev E 2016; 94:012127. [PMID: 27575096 DOI: 10.1103/physreve.94.012127] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2016] [Indexed: 06/06/2023]
Abstract
We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures T_{1} and T_{2} (<T_{1}), respectively. Particles are trapped by a harmonic potential and driven by a linear external force. The system can act as an autonomous heat engine performing work against the external driving force. Linearity of the system enables us to examine thermodynamic properties of the engine analytically. We find that the efficiency of the engine at maximum power η_{MP} is given by η_{MP}=1-sqrt[T_{2}/T_{1}]. This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of η_{MP} to nonendoreversible engines. We also obtain the large deviation function of the probability distribution for the stochastic efficiency in the overdamped limit. The large deviation function takes the minimum value at macroscopic efficiency η=η[over ¯] and increases monotonically until it reaches plateaus when η≤η_{L} and η≥η_{R} with model-dependent parameters η_{R} and η_{L}.
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Affiliation(s)
- Jong-Min Park
- Department of Physics, University of Seoul, Seoul 02504, Korea
| | - Hyun-Myung Chun
- Department of Physics, University of Seoul, Seoul 02504, Korea
| | - Jae Dong Noh
- Department of Physics, University of Seoul, Seoul 02504, Korea
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
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12
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Zheng Y, Hänggi P, Poletti D. Occurrence of discontinuities in the performance of finite-time quantum Otto cycles. Phys Rev E 2016; 94:012137. [PMID: 27575106 DOI: 10.1103/physreve.94.012137] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Indexed: 06/06/2023]
Abstract
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
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Affiliation(s)
- Yuanjian Zheng
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore
| | - Peter Hänggi
- Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstr. 4, D-80799 München, Germany
- Department of Physics, National University of Singapore, 117542 Singapore, Republic of Singapore
| | - Dario Poletti
- Engineering Product Development Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore
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13
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Quantum Coherent Three-Terminal Thermoelectrics: Maximum Efficiency at Given Power Output. ENTROPY 2016. [DOI: 10.3390/e18060208] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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14
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Proesmans K, Driesen C, Cleuren B, Van den Broeck C. Efficiency of single-particle engines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032105. [PMID: 26465424 DOI: 10.1103/physreve.92.032105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Indexed: 06/05/2023]
Abstract
We study the efficiency of a single-particle Szilard and Carnot engine. Within a first order correction to the quasistatic limit, the work distribution is found to be Gaussian and the correction factor to average work and efficiency only depends on the piston speed. The stochastic efficiency is studied for both models and the recent findings on efficiency fluctuations are confirmed numerically. Special features are revealed in the zero-temperature limit.
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Affiliation(s)
- Karel Proesmans
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
| | - Cedric Driesen
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
| | - Bart Cleuren
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
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