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Fei Z, Ma YH. Temperature fluctuations in mesoscopic systems. Phys Rev E 2024; 109:044101. [PMID: 38755872 DOI: 10.1103/physreve.109.044101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 02/26/2024] [Indexed: 05/18/2024]
Abstract
Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equation with respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.
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Affiliation(s)
- Zhaoyu Fei
- Department of Physics and Key Laboratory of Optical Field Manipulation of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou 310018, China
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
- Department of Physics, Beijing Normal University, Beijing 100875, China
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2
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Zhang ZZ, Tan QS, Wu W. Heat distribution in quantum Brownian motion. Phys Rev E 2023; 108:014138. [PMID: 37583192 DOI: 10.1103/physreve.108.014138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 07/11/2023] [Indexed: 08/17/2023]
Abstract
We investigate the heat statistics in a relaxation process of quantum Brownian motion described by the Caldeira-Leggett model. By employing the normal mode transformation and the phase-space formulation approach, we can analyze the quantum heat distribution within an exactly dynamical framework beyond the traditional paradigm of Born-Markovian and weak-coupling approximations. It is revealed that the exchange fluctuation theorem for quantum heat generally breaks down in the strongly non-Markovian regime. Our results may improve the understanding about the nonequilibrium thermodynamics of open quantum systems when the usual Markovian treatment is no longer appropriate.
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Affiliation(s)
- Ze-Zhou Zhang
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Qing-Shou Tan
- Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communication, College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414000, China
| | - Wei Wu
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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3
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Myers NM, Peña FJ, Cortés N, Vargas P. Multilayer Graphene as an Endoreversible Otto Engine. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13091548. [PMID: 37177093 PMCID: PMC10180394 DOI: 10.3390/nano13091548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Revised: 04/29/2023] [Accepted: 05/03/2023] [Indexed: 05/15/2023]
Abstract
We examine the performance of a finite-time, endoreversible Otto heat engine with a working medium of monolayer or multilayered graphene subjected to an external magnetic field. As the energy spectrum of multilayer graphene under an external magnetic field depends strongly on the number of layers, so too does its thermodynamic behavior. We show that this leads to a simple relationship between the engine efficiency and the number of layers of graphene in the working medium. Furthermore, we find that the efficiency at maximum power for bilayer and trilayer working mediums can exceed that of a classical endoreversible Otto cycle. Conversely, a working medium of monolayer graphene displays identical efficiency at maximum power to a classical working medium. These results demonstrate that layered graphene can be a useful material for the construction of efficient thermal machines for diverse quantum device applications.
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Affiliation(s)
- Nathan M Myers
- Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA
| | - Francisco J Peña
- Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 11520, Chile
- Millennium Nucleus in NanoBioPhysics (NNBP), Av. España 1680, Valparaíso 11520, Chile
| | - Natalia Cortés
- Instituto de Alta Investigación, Universidad de Tarapacá, Arica Casilla 7D, Chile
- Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701, USA
| | - Patricio Vargas
- Departamento de Física, CEDENNA, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 11520, Chile
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Zhai RX, Cui FM, Ma YH, Sun CP, Dong H. Experimental test of power-efficiency trade-off in a finite-time Carnot cycle. Phys Rev E 2023; 107:L042101. [PMID: 37198805 DOI: 10.1103/physreve.107.l042101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 03/15/2023] [Indexed: 05/19/2023]
Abstract
The Carnot cycle is a prototype of an ideal heat engine cycle to draw mechanical energy from the heat flux between two thermal baths with the maximum efficiency, dubbed as the Carnot efficiency η_{C}. Such efficiency is reached by thermodynamical equilibrium processes with infinite time, accompanied unavoidably with vanishing power-energy output per unit time. The quest to acquire high power leads to an open question of whether a fundamental maximum efficiency exists for finite-time heat engines with given power. We experimentally implement a finite-time Carnot cycle with sealed dry air as a working substance and verify the existence of a trade-off relation between power and efficiency. Efficiency up to (0.524±0.034)η_{C} is reached for the engine to generate the maximum power, consistent with the theoretical prediction η_{C}/2. Our experimental setup shall provide a platform for studying finite-time thermodynamics consisting of nonequilibrium processes.
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Affiliation(s)
- Ruo-Xun Zhai
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Fang-Ming Cui
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
- Beijing Normal University, Beijing 100875, China
| | - Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - C P Sun
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Hui Dong
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
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Chen JF, Quan HT. Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs. Phys Rev E 2023; 107:024135. [PMID: 36932622 DOI: 10.1103/physreve.107.024135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 02/09/2023] [Indexed: 06/18/2023]
Abstract
For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.
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Affiliation(s)
- Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
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Guéry-Odelin D, Jarzynski C, Plata CA, Prados A, Trizac E. Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:035902. [PMID: 36535018 DOI: 10.1088/1361-6633/acacad] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 12/19/2022] [Indexed: 06/17/2023]
Abstract
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.
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Affiliation(s)
- David Guéry-Odelin
- Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, CNRS, Toulouse, France
| | - Christopher Jarzynski
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, United States of America
- Institute for Physical Science and Technology, University of Maryland, College Park, MD, United States of America
- Department of Physics, University of Maryland, College Park, MD, United States of America
| | - Carlos A Plata
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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Zhao XH, Gong ZN, Tu ZC. Low-dissipation engines: Microscopic construction via shortcuts to adiabaticity and isothermality, the optimal relation between power and efficiency. Phys Rev E 2022; 106:064117. [PMID: 36671114 DOI: 10.1103/physreve.106.064117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Accepted: 11/27/2022] [Indexed: 06/17/2023]
Abstract
We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical formula of the efficiency at maximum power with explicit expressions of dissipation coefficients under the optimized protocols. When the relative temperature difference between the two baths in the cycle is insignificant, this expression satisfies the universal law of efficiency at maximum power up to the quadratic term of the Carnot efficiency. For large relative temperature differences, the efficiency at maximum power tends to be 1/2. Furthermore, we analyze the issue of power at any given efficiency for general low-dissipation engines and then obtain the supremum of the power in three limiting cases, respectively. These expressions of maximum power at given efficiency provide the optimal relations between power and efficiency which are tighter than the results in previous references.
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Affiliation(s)
- Xiu-Hua Zhao
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | | | - Z C Tu
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Chen JF. Optimizing Brownian heat engine with shortcut strategy. Phys Rev E 2022; 106:054108. [PMID: 36559462 DOI: 10.1103/physreve.106.054108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 10/20/2022] [Indexed: 06/17/2023]
Abstract
Shortcuts to isothermality provide a powerful method to speed up quasistatic thermodynamic processes within finite-time manipulation. We employ the shortcut strategy to design and optimize Brownian heat engines, and we formulate a geometric description of the energetics with the thermodynamic length. We obtain a tight and reachable bound of the output power for shortcut-driven heat engines. The bound is reached by the optimal shortcut protocol to vary the control parameters with a proper constant velocity of the thermodynamic length. With the shortcut strategy, we optimize the control of Brownian heat engines to achieve the maximum power in the general-damped situation. We also derive the efficiency at the maximum power and the maximum power at the given efficiency for shortcut-driven heat engines.
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Affiliation(s)
- Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China
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