1
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Kasuga K, Yoshimori A. Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation. Phys Rev E 2023; 108:034109. [PMID: 37849163 DOI: 10.1103/physreve.108.034109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 08/15/2023] [Indexed: 10/19/2023]
Abstract
We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equation with a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equation describing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.
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Affiliation(s)
- Kotaro Kasuga
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
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2
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Xiao Y, Li K, He J, Wang J. Performance of Quantum Heat Engines Enhanced by Adiabatic Deformation of Trapping Potential. ENTROPY (BASEL, SWITZERLAND) 2023; 25:484. [PMID: 36981372 PMCID: PMC10048115 DOI: 10.3390/e25030484] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 03/05/2023] [Accepted: 03/06/2023] [Indexed: 06/18/2023]
Abstract
We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, η*=ηC/2+ηC2/8+O(ηC3), where ηC=1-βhr/βcr is the Carnot efficiency, with βhr(βcr) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator.
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Affiliation(s)
- Yang Xiao
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Kai Li
- 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, Department of Physics, Fudan University, Shanghai 200433, China
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3
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Eglinton J, Brandner K. Geometric bounds on the power of adiabatic thermal machines. Phys Rev E 2022; 105:L052102. [PMID: 35706185 DOI: 10.1103/physreve.105.l052102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
We analyze the performance of slowly driven meso- and microscale refrigerators and heat engines that operate between two thermal baths with a small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasistatic limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.
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Affiliation(s)
- Joshua Eglinton
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Kay Brandner
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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4
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Yuan H, Ma YH, Sun CP. Optimizing thermodynamic cycles with two finite-sized reservoirs. Phys Rev E 2022; 105:L022101. [PMID: 35291152 DOI: 10.1103/physreve.105.l022101] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
We study the nonequilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time τ is bounded from below by the entropy production σ_{min}∝1/τ. We discover a general power-efficiency tradeoff depending on the ratio of heat capacities (γ) of the reservoirs for the engine, and a universal efficiency at maximum average power of the engine for arbitrary γ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with σ_{min} is demonstrated. Our findings can be used to develop a general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.
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Affiliation(s)
- Hong Yuan
- Graduate School of China Academy of Engineering Physics, Number 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, Number 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - C P Sun
- Graduate School of China Academy of Engineering Physics, Number 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
- Beijing Computational Science Research Center, Beijing 100193, China
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5
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Lee JS, Park JM, Park H. Universal form of thermodynamic uncertainty relation for Langevin dynamics. Phys Rev E 2021; 104:L052102. [PMID: 34942785 DOI: 10.1103/physreve.104.l052102] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 10/19/2021] [Indexed: 11/07/2022]
Abstract
The thermodynamic uncertainty relation (TUR) provides a stricter bound for entropy production (EP) than that of the thermodynamic second law. This stricter bound can be utilized to infer the EP and derive other tradeoff relations. Though the validity of the TUR has been verified in various stochastic systems, its application to general Langevin dynamics has not been successfully unified, especially for underdamped Langevin dynamics, where odd parity variables in time-reversal operation such as velocity get involved. Previous TURs for underdamped Langevin dynamics are neither experimentally accessible nor reduced to the original form of the overdamped Langevin dynamics in the zero-mass limit. Here, we find a TUR for underdamped Langevin dynamics with an arbitrary time-dependent protocol, which is operationally accessible when all mechanical forces are controllable. We show that the original TUR is a consequence of our underdamped TUR in the zero-mass limit. This indicates that the TUR formulation presented here can be regarded as the universal form of the TUR for general Langevin dynamics.
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Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
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6
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Izumida Y. Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines. Phys Rev E 2021; 103:L050101. [PMID: 34134349 DOI: 10.1103/physreve.103.l050101] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 04/19/2021] [Indexed: 11/07/2022]
Abstract
In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global and local Onsager coefficients, defined over one cycle and at any instant of a cycle, respectively, is not derived. To address this limitation, we develop a linear response theory for the speed of adiabatically changing parameters and temperature differences in generic Gaussian heat engines obeying Fokker-Planck dynamics. We establish a hierarchical relationship between the global linear response relations, defined over one cycle of the heat engines, and the local ones, defined at any instant of the cycle. This yields a detailed expression for the global Onsager coefficients in terms of the local Onsager coefficients. Moreover, we derive an efficiency bound, which is tighter than the Carnot bound, for adiabatically driven linear irreversible heat engines based on the detailed global Onsager coefficients. Finally, we demonstrate the application of the theory using the simplest stochastic Brownian heat engine model.
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Affiliation(s)
- Yuki Izumida
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan
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7
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Giordano S. Entropy production and Onsager reciprocal relations describing the relaxation to equilibrium in stochastic thermodynamics. Phys Rev E 2021; 103:052116. [PMID: 34134271 DOI: 10.1103/physreve.103.052116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 04/27/2021] [Indexed: 06/12/2023]
Abstract
We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by evaluating the entropy production and the relation between fluxes and forces in a harmonic system with N particles in contact with N different reservoirs. We suppose that the system is in a nonequilibrium stationary state in a first phase and we study the relaxation to equilibrium in a second phase. During this relaxation, we can identify the linear relation between fluxes and forces satisfying the Onsager reciprocity and we obtain a nonlinear expression for the entropy production. Only when forces and fluxes are small does the entropic production turn into a quadratic form in the forces, as predicted by the Onsager theory.
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Affiliation(s)
- Stefano Giordano
- Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520 - IEMN - Institut d'Électronique de Microélectronique et de Nanotechnologie, LIA LICS/LEMAC, F-59000 Lille, France
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8
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Bonança MVS, Nazé P, Deffner S. Negative entropy production rates in Drude-Sommerfeld metals. Phys Rev E 2021; 103:012109. [PMID: 33601516 DOI: 10.1103/physreve.103.012109] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 12/17/2020] [Indexed: 11/07/2022]
Abstract
It is commonly accepted that in typical situations the rate of entropy production is non-negative. We show that this assertion is not entirely correct, not even in the linear regime, if a time-dependent, external perturbation is not compensated by a rapid enough decay of the response function. This is demonstrated for three variants of the Drude model to describe electrical conduction in noble metals, namely the classical free electron gas, the Drude-Sommerfeld model, and the extended Drude-Sommerfeld model. The analysis is concluded with a discussion of potential experimental verifications and ramifications of negative entropy production rates.
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Affiliation(s)
- Marcus V S Bonança
- Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil
| | - Pierre Nazé
- Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil
| | - Sebastian Deffner
- Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil.,Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
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9
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Izumida Y. Quasilinear irreversible thermodynamics of a low-temperature-differential kinematic Stirling heat engine. Phys Rev E 2020; 102:012142. [PMID: 32795077 DOI: 10.1103/physreve.102.012142] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 06/26/2020] [Indexed: 11/07/2022]
Abstract
Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important sustainable energy technology. The author recently proposed a nonlinear dynamics model of an LTD kinematic Stirling heat engine to study the rotational mechanism of the engine [Y. Izumida, Europhys. Lett. 121, 50004 (2018)EULEEJ0295-507510.1209/0295-5075/121/50004]. This paper presents our study of the nonequilibrium thermodynamics analysis of this engine model, where a load torque against which the engine does work is introduced. We demonstrate that the engine's rotational state is in a quasilinear response regime where the thermodynamic fluxes show a linear dependence on the thermodynamic forces. Significantly, it is found that the response coefficients of the quasilinear relations are symmetric, which is similar to Onsager symmetry in linear irreversible thermodynamics. Based on these relations, we formulate the maximum efficiency of the engine. We also elucidate that the symmetry of the quasilinear response coefficients emerges by reflecting the (anti-)reciprocity of the Onsager kinetic coefficients identified for the relaxation dynamics of the engine in the vicinity of an equilibrium state. We expect that the present study will pave the way for developing nonequilibrium thermodynamics of autonomous heat engines described as a nonlinear dynamical system.
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Affiliation(s)
- Yuki Izumida
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan
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10
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Lee JS, Park JM, Chun HM, Um J, Park H. Exactly solvable two-terminal heat engine with asymmetric Onsager coefficients: Origin of the power-efficiency bound. Phys Rev E 2020; 101:052132. [PMID: 32575278 DOI: 10.1103/physreve.101.052132] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2020] [Accepted: 04/30/2020] [Indexed: 11/07/2022]
Abstract
An engine producing a finite power at the ideal (Carnot) efficiency is a dream engine which is not prohibited by the thermodynamic second law. Some years ago, a two-terminal heat engine with asymmetric Onsager coefficients in the linear response regime was suggested by Benenti et al. [Phys. Rev. Lett. 106, 230602 (2011)10.1103/PhysRevLett.106.230602], as a prototypical system to make such a dream come true with nondivergent system parameter values. However, such a system has never been realized, in spite of many trials. Here, we introduce an exactly solvable two-terminal Brownian heat engine with the asymmetric Onsager coefficients in the presence of a Lorenz (magnetic) force. Nevertheless, we show that the dream engine regime cannot be accessible, even with the asymmetric Onsager coefficients, due to an instability keeping the engine from reaching its steady state. This is consistent with recent tradeoff relations between the engine power and efficiency, where the (cyclic) steady-state condition is implicitly presumed. We conclude that the inaccessibility to the dream engine originates from the steady-state constraint on the engine.
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Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyun-Myung Chun
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jaegon Um
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
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11
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Brandner K, Saito K. Thermodynamic Geometry of Microscopic Heat Engines. PHYSICAL REVIEW LETTERS 2020; 124:040602. [PMID: 32058746 DOI: 10.1103/physrevlett.124.040602] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Indexed: 06/10/2023]
Abstract
We develop a general framework to describe the thermodynamics of microscopic heat engines driven by arbitrary periodic temperature variations and modulations of a mechanical control parameter. Within the slow-driving regime, our approach leads to a universal trade-off relation between efficiency and power, which follows solely from geometric arguments and holds for any thermodynamically consistent microdynamics. Focusing on Lindblad dynamics, we derive a second bound showing that coherence as a genuine quantum effect inevitably reduces the performance of slow engine cycles regardless of the driving amplitudes. To show how our theory can be applied in practice, we work out a specific example, which lies within the range of current solid-state technologies.
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Affiliation(s)
- Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
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12
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Lee JS, Park JM, Park H. Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force. Phys Rev E 2019; 100:062132. [PMID: 31962517 DOI: 10.1103/physreve.100.062132] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Indexed: 06/10/2023]
Abstract
Recently, it has been shown that there is a trade-off relation between thermodynamic cost and current fluctuations, referred to as the thermodynamic uncertainty relation (TUR). The TUR has been derived for various processes, such as discrete-time Markov jump processes and overdamped Langevin dynamics. For underdamped dynamics, it has recently been reported that some modification is necessary for application of the TUR. However, the previous TUR for underdamped dynamics is not applicable to a system driven by a velocity-dependent force. In this study, we present a TUR, applicable to a system driven by a velocity-dependent force in the context of underdamped Langevin dynamics, by extending the theory of Vu and Hasegawa [Phys. Rev. E 100, 032130 (2019)2470-004510.1103/PhysRevE.100.032130]. We show that our TUR accurately describes the trade-off properties of a molecular refrigerator (cold damping), Brownian dynamics in a magnetic field, and an active particle system.
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Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
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13
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Proesmans K, Fiore CE. General linear thermodynamics for periodically driven systems with multiple reservoirs. Phys Rev E 2019; 100:022141. [PMID: 31574599 DOI: 10.1103/physreve.100.022141] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 11/07/2022]
Abstract
We derive a linear thermodynamics theory for general Markov dynamics with both steady-state and time-periodic drivings. Expressions for thermodynamic quantities, such as chemical work, heat, and entropy production are obtained in terms of equilibrium probability distribution and the drivings. The entropy production is derived as a bilinear function of thermodynamic forces and the associated fluxes. We derive explicit formulae for the Onsager coefficients and use them to verify the Onsager-Casimir reciprocal relations. Our results are illustrated on a periodically driven quantum dot in contact with two electron reservoirs and optimization protocols are discussed.
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Affiliation(s)
| | - Carlos E Fiore
- Institute of Physics of São Paulo University, Rua do Matão, 1371, 05508-090 São Paulo, SP, Brazil
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14
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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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15
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Rosas A, Van den Broeck C, Lindenberg K. Three-stage stochastic pump: Another type of Onsager-Casimir symmetry and results far from equilibrium. Phys Rev E 2018; 97:062103. [PMID: 30011430 DOI: 10.1103/physreve.97.062103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2018] [Indexed: 06/08/2023]
Abstract
The stochastic thermodynamic analysis of a time-periodic single particle pump sequentially exposed to three thermochemical reservoirs is presented. The analysis provides explicit results for flux, thermodynamic force, entropy production, work, and heat. These results apply near equilibrium as well as far from equilibrium. In the linear response regime, a different type of Onsager-Casimir symmetry is uncovered. The Onsager matrix becomes symmetric in the limit of zero dissipation.
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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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16
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Frezzato D. Dissipation, lag, and drift in driven fluctuating systems. Phys Rev E 2018; 96:062113. [PMID: 29347343 DOI: 10.1103/physreve.96.062113] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Indexed: 11/07/2022]
Abstract
This work deals with thermostated fluctuating systems subjected to driven transformations of the internal energetics. The main focus is on generally multidimensional systems with continuous configurational degrees of freedom over which overdamped Markovian fluctuations take place (diffusive regime of the motion). Mutual bounds are established between the average energy dissipation, the deviation between nonequilibrium probability density and underlying equilibrium distribution due to the system's lag, and the statistical properties of the components of the directed flow induced by the transformation itself. The directed flow is here expressed in terms of time-dependent "drift velocity" associated with the probability current in a advection-like formulation of the nonstationary Fokker-Planck equation. Consideration of the drift makes that the bounds achieved here extend the inequality derived by Vaikuntanathan and Jarzynski [Europhys. Lett. 87, 60005 (2009)EULEEJ0295-507510.1209/0295-5075/87/60005] involving only dissipation and lag. The key relations are then specified for the so-called stochastic pumps, i.e., systems that reach a periodic steady state in response of cyclic transformations and that are prototypes of nonautonomous dissipative converters of input energy into directed motion; a one-dimensional case model is adopted to illustrate the main features. Complementary results concerning bounds between the evolution rates of dissipation and lag, valid for both overdamped and underdamped dynamics, are also presented.
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Affiliation(s)
- Diego Frezzato
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131, Padova, Italy
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17
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Iyyappan I, Ponmurugan M. General relations between the power, efficiency, and dissipation for the irreversible heat engines in the nonlinear response regime. Phys Rev E 2018; 97:012141. [PMID: 29448419 DOI: 10.1103/physreve.97.012141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Indexed: 06/08/2023]
Abstract
We derive the general relations between the maximum power, maximum efficiency, and minimum dissipation for the irreversible heat engine in a nonlinear response regime. In this context, we use the minimally nonlinear irreversible model and obtain the lower and upper bounds of the above relations for the asymmetric dissipation limits. These relations can be simplified further when the system possesses the time-reversal symmetry or antisymmetry. We find that our results are the generalization of various such relations obtained earlier for different heat engines.
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Affiliation(s)
- I Iyyappan
- Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu, Thiruvarur 610 005, Tamil Nadu, India
| | - M Ponmurugan
- Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu, Thiruvarur 610 005, Tamil Nadu, India
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18
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Holubec V, Ryabov A. Diverging, but negligible power at Carnot efficiency: Theory and experiment. Phys Rev E 2017; 96:062107. [PMID: 29347419 DOI: 10.1103/physreve.96.062107] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Indexed: 11/07/2022]
Abstract
We discuss the possibility of reaching the Carnot efficiency by heat engines (HEs) out of quasistatic conditions at nonzero power output. We focus on several models widely used to describe the performance of actual HEs. These models comprise quantum thermoelectric devices, linear irreversible HEs, minimally nonlinear irreversible HEs, HEs working in the regime of low-dissipation, overdamped stochastic HEs and an underdamped stochastic HE. Although some of these HEs can reach the Carnot efficiency at nonzero and even diverging power, the magnitude of this power is always negligible compared to the maximum power attainable in these systems. We provide conditions for attaining the Carnot efficiency in the individual models and explain practical aspects connected with reaching the Carnot efficiency at large power output. Furthermore, we show how our findings can be tested in practice using a standard Brownian HE realizable with available micromanipulation techniques.
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Affiliation(s)
- Viktor Holubec
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany.,Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
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19
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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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20
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Ray S, Barato AC. Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes. Phys Rev E 2017; 96:052120. [PMID: 29347722 DOI: 10.1103/physreve.96.052120] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Indexed: 06/07/2023]
Abstract
Periodic driving is used to operate machines that go from standard macroscopic engines to small nonequilibrium microsized systems. Two classes of such systems are small heat engines driven by periodic temperature variations, and molecular pumps driven by external stimuli. Well-known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities, and symmetry relations for the Onsager coefficients from linear-response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients, and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.
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Affiliation(s)
- Somrita Ray
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Strasse 38, 01187 Dresden, Germany
| | - Andre C Barato
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Strasse 38, 01187 Dresden, Germany
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21
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Brandner K, Bauer M, Seifert U. Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response. PHYSICAL REVIEW LETTERS 2017; 119:170602. [PMID: 29219425 DOI: 10.1103/physrevlett.119.170602] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2017] [Indexed: 06/07/2023]
Abstract
We identify a universal indicator for the impact of coherence on periodically driven quantum devices by dividing their power output into a classical contribution and one stemming solely from superpositions. Specializing to Lindblad dynamics and small driving amplitudes, we derive general upper bounds on both the coherent and the total power of cyclic heat engines. These constraints imply that, for sufficiently slow driving, coherence inevitably leads to power losses in the linear-response regime. We illustrate our theory by working out the experimentally relevant example of a single-qubit engine.
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Affiliation(s)
- Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Michael Bauer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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22
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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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23
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Holubec V, Ryabov A. Work and power fluctuations in a critical heat engine. Phys Rev E 2017; 96:030102. [PMID: 29347002 DOI: 10.1103/physreve.96.030102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2017] [Indexed: 06/07/2023]
Abstract
We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016)2041-172310.1038/ncomms11895]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.
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Affiliation(s)
- Viktor Holubec
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-180 00 Praha, Czech Republic
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24
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Shiraishi N, Tajima H. Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound. Phys Rev E 2017; 96:022138. [PMID: 28950461 DOI: 10.1103/physreve.96.022138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2017] [Indexed: 06/07/2023]
Abstract
A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.
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Affiliation(s)
- Naoto Shiraishi
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
| | - Hiroyasu Tajima
- Center for Emergent Matter Science (CEMS), RIKEN, 2-1 Hirosawa, Wako, 351-0198 Japan
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25
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Wang H, He J, Wang J. Endoreversible quantum heat engines in the linear response regime. Phys Rev E 2017; 96:012152. [PMID: 29347192 DOI: 10.1103/physreve.96.012152] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Indexed: 06/07/2023]
Abstract
We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.
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Affiliation(s)
- Honghui Wang
- 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 Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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26
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Izumida Y, Okuda K. Molecular kinetic analysis of a local equilibrium Carnot cycle. Phys Rev E 2017; 96:012123. [PMID: 29347144 DOI: 10.1103/physreve.96.012123] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 06/07/2023]
Abstract
We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a Maxwell-Boltzmann distribution with a spatially uniform temperature and a spatially varying local center-of-mass velocity. We construct the local equilibrium Carnot cycle of an ideal gas, based on this distribution, and show that the efficiency of the present cycle is given by the endoreversible Carnot efficiency using the molecular kinetic temperatures of the gas. We also obtain an analytic expression of the efficiency at maximum power of our cycle under a small temperature difference. Our theory is also confirmed by a molecular dynamics simulation.
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Affiliation(s)
- Yuki Izumida
- Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan
| | - Koji Okuda
- Division of Physics, Hokkaido University, Sapporo 060-0810, Japan
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27
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Rosas A, Van den Broeck C, Lindenberg K. Onsager coefficients for systems with periodic potentials. Phys Rev E 2016; 94:052129. [PMID: 27967176 DOI: 10.1103/physreve.94.052129] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 11/07/2022]
Abstract
We carry out the thermodynamic analysis of a Markovian stochastic engine, driven by a spatially and temporally periodic modulation in a d-dimensional space. We derive the analytic expressions for the Onsager coefficients characterizing the linear response regime for the isothermal transfer of one type of work (a driver) to another (a load), mediated by a stochastic time-periodic machine. As an illustration, we obtain the explicit results for a Markovian kangaroo process coupling two orthogonal directions and find extremely good agreement with numerical simulations. In addition, we obtain and discuss expressions for the entropy production, power, and efficiency for the kangaroo process.
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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, BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA
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28
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Shiraishi N, Saito K, Tasaki H. Universal Trade-Off Relation between Power and Efficiency for Heat Engines. PHYSICAL REVIEW LETTERS 2016; 117:190601. [PMID: 27858428 DOI: 10.1103/physrevlett.117.190601] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
For a general thermodynamic system described as a Markov process, we prove a general lower bound for dissipation in terms of the square of the heat current, thus establishing that nonvanishing current inevitably implies dissipation. This leads to a universal trade-off relation between efficiency and power, with which we rigorously prove that a heat engine with nonvanishing power never attains the Carnot efficiency. Our theory applies to systems arbitrarily far from equilibrium, and does not assume any specific symmetry of the model.
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Affiliation(s)
- Naoto Shiraishi
- Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Keiji Saito
- Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
| | - Hal Tasaki
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
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29
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Yamamoto S, Ito S, Shiraishi N, Sagawa T. Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines. Phys Rev E 2016; 94:052121. [PMID: 27967007 DOI: 10.1103/physreve.94.052121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Indexed: 06/06/2023]
Abstract
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.
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Affiliation(s)
- Shumpei Yamamoto
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Sosuke Ito
- Department of Physics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
| | - Naoto Shiraishi
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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30
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Camerin F, Frezzato D. Fluctuating systems under cyclic perturbations: Relation between energy dissipation and intrinsic relaxation processes. Phys Rev E 2016; 94:022117. [PMID: 27627256 DOI: 10.1103/physreve.94.022117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 11/07/2022]
Abstract
This study focuses on fluctuating classical systems in contact with a thermal bath, and whose configurational energetics undergoes cyclic transformations due to interaction with external perturbing agents. Under the assumptions that the configurational dynamics is a stochastic Markov process in the overdamped regime and that the nonequilibrium configurational distribution remains close to the underlying equilibrium one, we derived an analytic approximation of the average dissipated energy per cycle in the asymptotic limit (i.e., after many cycles of perturbation). The energy dissipation is then readily translated into average entropy production, per cycle, in the environment. The accuracy of the approximation was tested by comparing the outcomes with the exact values obtained by stochastic simulations of a model case: a "particle on a ring" that fluctuates in a bistable potential perturbed in two different ways. As pointed out in previous studies on the stochastic resonance phenomenon, the dependence of the average dissipation on the perturbation period may unveil the inner spectrum of the system's fluctuation rates. In this respect, the analytical approximation presented here makes it possible to unveil the connection between average dissipation, intrinsic rates and modes of fluctuation of the system at the unperturbed equilibrium, and features of the perturbation itself (namely, the period of the cycle and the projections of the energy perturbation over the system's modes). The possibilities of employing the analytical results as a guide to devising and rationalizing a sort of "spectroscopic calorimetry" experiment, and of employing them in strategies aiming to optimize the system's features on the basis of a target average dissipation, are briefly discussed.
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Affiliation(s)
- Fabrizio Camerin
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131, Padova, Italy
| | - Diego Frezzato
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131, Padova, Italy
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31
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Abstract
Since its inception about two centuries ago thermodynamics has sparkled continuous interest and fundamental questions. According to the second law no heat engine can have an efficiency larger than Carnot's efficiency. The latter can be achieved by the Carnot engine, which however ideally operates in infinite time, hence delivers null power. A currently open question is whether the Carnot efficiency can be achieved at finite power. Most of the previous works addressed this question within the Onsager matrix formalism of linear response theory. Here we pursue a different route based on finite-size-scaling theory. We focus on quantum Otto engines and show that when the working substance is at the verge of a second order phase transition diverging energy fluctuations can enable approaching the Carnot point without sacrificing power. The rate of such approach is dictated by the critical indices, thus showing the universal character of our analysis. The second law of thermodynamics says that the efficiency of a heat engine is limited by the Carnot efficiency. Here, the authors use finite-size-scaling theory to investigate whether this ultimate limit can be achieved at finite power using quantum Otto engines.
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32
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Proesmans K, Cleuren B, Van den Broeck C. Power-Efficiency-Dissipation Relations in Linear Thermodynamics. PHYSICAL REVIEW LETTERS 2016; 116:220601. [PMID: 27314707 DOI: 10.1103/physrevlett.116.220601] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Indexed: 06/06/2023]
Abstract
We derive general relations between the maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics. The relations simplify further in the presence of a particular symmetry of the Onsager matrix, which can be derived from detailed balance. The results are illustrated on a periodically driven system and a three-terminal device subject to an external magnetic field.
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33
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Brandner K, Seifert U. Periodic thermodynamics of open quantum systems. Phys Rev E 2016; 93:062134. [PMID: 27415235 DOI: 10.1103/physreve.93.062134] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2016] [Indexed: 06/06/2023]
Abstract
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
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Affiliation(s)
- Kay Brandner
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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34
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Raz O, Subaşı Y, Pugatch R. Geometric Heat Engines Featuring Power that Grows with Efficiency. PHYSICAL REVIEW LETTERS 2016; 116:160601. [PMID: 27152782 DOI: 10.1103/physrevlett.116.160601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Indexed: 06/05/2023]
Abstract
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
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Affiliation(s)
- O Raz
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
| | - Y Subaşı
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
| | - R Pugatch
- Simons Center for Systems Biology, School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
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35
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Bauer M, Brandner K, Seifert U. Optimal performance of periodically driven, stochastic heat engines under limited control. Phys Rev E 2016; 93:042112. [PMID: 27176259 DOI: 10.1103/physreve.93.042112] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Indexed: 06/05/2023]
Abstract
We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows us to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.
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Affiliation(s)
- Michael Bauer
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Kay Brandner
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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36
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Cerino L, Puglisi A, Vulpiani A. Linear and nonlinear thermodynamics of a kinetic heat engine with fast transformations. Phys Rev E 2016; 93:042116. [PMID: 27176263 DOI: 10.1103/physreve.93.042116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2016] [Indexed: 06/05/2023]
Abstract
We investigate a kinetic heat engine model composed of particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period τ: their relative excursions, δ and ε, respectively, constitute the thermodynamic forces dragging the system out of equilibrium. The analysis of the entropy production of the system allows us to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small δ and ε the fluxes are linear in the forces through a τ-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which-in the linear regime-yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e., outside of the linear regime. In all our analysis the adiabatic limit τ→∞ and the the small-force limit δ,ε→0 are not directly related.
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Affiliation(s)
- Luca Cerino
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 2, 00185 Rome, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 2, 00185 Rome, Italy
| | - Angelo Vulpiani
- Istituto dei Sistemi Complessi-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P. le Aldo Moro 2, 00185 Rome, Italy
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37
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Wang Y. Optimizing work output for finite-sized heat reservoirs: Beyond linear response. Phys Rev E 2016; 93:012120. [PMID: 26871037 DOI: 10.1103/physreve.93.012120] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2015] [Indexed: 06/05/2023]
Abstract
We uncover an optimization principle for the finite-time heat-work conversion process performed between two finite-sized heat reservoirs in the nonlinear response regime that is characterized by rather generic flux-force relations. We solve the problem of maximizing work output in a given time interval by means of the variational method. Moreover, in the limiting case that the cold reservoir is infinite, we find the corresponding optimized process can be determined by a single quantity, which plays the role similar to that of the Hamiltonian in classical mechanics. Some theoretical implications are discussed consequently, under the generalized tight-coupling condition which applies to both linear and nonlinear response cases. Our results can hopefully help design and control realistic thermodynamical processes.
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Affiliation(s)
- Yan Wang
- School of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
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