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Wang Z, Ren J. Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport. PHYSICAL REVIEW LETTERS 2024; 132:207101. [PMID: 38829089 DOI: 10.1103/physrevlett.132.207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 09/06/2023] [Accepted: 04/11/2024] [Indexed: 06/05/2024]
Abstract
Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.
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Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, 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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Wang Z, Chen J, Ren J. Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion. Phys Rev E 2022; 106:L032102. [PMID: 36266907 DOI: 10.1103/physreve.106.l032102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.
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Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jiangzhi Chen
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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Liao Z, Vaikuntanathan S. Energy rectification in active gyroscopic networks under time-periodic modulations. Phys Rev E 2021; 104:014601. [PMID: 34412249 DOI: 10.1103/physreve.104.014601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
Combinations of gyroscopic forces and nonequilibrium activity have been explored recently in rectifying energy in networks with complex geometries and topologies [Phys. Rev. X 10, 021036 (2020)2160-330810.1103/PhysRevX.10.021036]. Based on this previous work, here we study the effect of added time-periodic modulations. Numerical calculations show that the time-modulated network generates net energy transport between sites and the surroundings, even in the absence of any temperature gradients. Combining path integral formulation and diagrammatic expansion, we explain how such anomalous energy transport emerges, and show how the transport pattern in complex networks can be connected to relatively simple local structures.
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Affiliation(s)
- Zhenghan Liao
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
| | - Suriyanarayanan Vaikuntanathan
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA.,James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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Xu L, Yang S, Huang J. Dipole-assisted thermotics: Experimental demonstration of dipole-driven thermal invisibility. Phys Rev E 2020; 100:062108. [PMID: 31962417 DOI: 10.1103/physreve.100.062108] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2019] [Indexed: 11/07/2022]
Abstract
Thermal management has made considerable progress in the past decade for the emerging field of thermal metamaterials. However, two severe problems still handicap the development of thermal metamaterials. That is, thermal conductivities should be singular and uncommon as required by corresponding theories. To solve these problems, here we establish the theory of dipole-assisted thermotics. By tailoring the thermal dipole moment, thermal invisibility can be achieved without the requirements of singular and uncommon thermal conductivities. Furthermore, finite-element simulations and laboratory experiments both validate the theoretical analyses. The performance of the dipole-driven scheme is excellent in both two and three dimensions, and in both steady and transient states. Dipole-assisted thermotics not only offers a distinct mechanism to achieve thermal invisibility, but also has potential applications in thermal management such as infrared signature reduction, thermal protection, and infrared camouflage.
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Affiliation(s)
- Liujun Xu
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
| | - Shuai Yang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
| | - Jiping Huang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
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Latella I, Messina R, Rubi JM, Ben-Abdallah P. Radiative Heat Shuttling. PHYSICAL REVIEW LETTERS 2018; 121:023903. [PMID: 30085727 DOI: 10.1103/physrevlett.121.023903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate the existence of a shuttling effect for the radiative heat flux exchanged between two bodies separated by a vacuum gap when the chemical potential of photons or the temperature difference is modulated. We show that this modulation typically gives rise to a supplementary flux which superimposes to the flux produced by the mean gradient, enhancing the heat exchange. When the system displays a negative differential thermal resistance, however, the radiative shuttling contributes to insulate the two bodies from each other. These results pave the way for a novel strategy for an active management of radiative heat exchanges in nonequilibrium systems.
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Affiliation(s)
- Ivan Latella
- Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, PQ J1K 2R1, Canada
| | - Riccardo Messina
- Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, 2 Avenue Augustin Fresnel, 91127 Palaiseau Cedex, France
| | - J Miguel Rubi
- Secció de Física Estadística i Interdisciplinària-Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franqués 1, 08028 Barcelona, Spain
| | - Philippe Ben-Abdallah
- Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, PQ J1K 2R1, Canada
- Laboratoire Charles Fabry, UMR 8501, Institut d'Optique, CNRS, Université Paris-Saclay, 2 Avenue Augustin Fresnel, 91127 Palaiseau Cedex, France
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Liu S, Agarwalla BK, Wang JS, Li B. Classical heat transport in anharmonic molecular junctions: exact solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022122. [PMID: 23496475 DOI: 10.1103/physreve.87.022122] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2012] [Indexed: 06/01/2023]
Abstract
We study full counting statistics for classical heat transport through anharmonic or nonlinear molecular junctions formed by interacting oscillators. An analytical result of the steady-state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of a temperature-dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two system parameters are modulated adiabatically. We present an anharmonic example for which all cumulants for heat can be obtained exactly. For a bounded single oscillator model with mass we found that the cumulants are independent of the nonlinear potential.
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Affiliation(s)
- Sha Liu
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546.
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