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Mohanta S, Saha M, Venkatesh BP, Agarwalla BK. Bounds on nonequilibrium fluctuations for asymmetrically driven quantum Otto engines. Phys Rev E 2023; 108:014118. [PMID: 37583162 DOI: 10.1103/physreve.108.014118] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Accepted: 06/21/2023] [Indexed: 08/17/2023]
Abstract
For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on nonequilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of nonequilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish a hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reverse cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.
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Affiliation(s)
- Sandipan Mohanta
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Madhumita Saha
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - B Prasanna Venkatesh
- Department of Physics, Indian Institute of Technology Gandhinagar, Palaj, Gujarat 382355, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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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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Zou CJ, Li Y, Xu JK, You JB, Png CE, Yang WL. Geometrical Bounds on Irreversibility in Squeezed Thermal Bath. ENTROPY (BASEL, SWITZERLAND) 2023; 25:128. [PMID: 36673269 PMCID: PMC9858152 DOI: 10.3390/e25010128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Revised: 12/23/2022] [Accepted: 01/05/2023] [Indexed: 06/17/2023]
Abstract
Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.
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Affiliation(s)
- Chen-Juan Zou
- Research Center of Nonlinear Science, School of Mathematical and Physical Science, Wuhan Textile University, Wuhan 430200, China
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yue Li
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Jia-Kun Xu
- Research Center of Nonlinear Science, School of Mathematical and Physical Science, Wuhan Textile University, Wuhan 430200, China
| | - Jia-Bin You
- Institute of High Performance Computing, Agency for Science, Technology, and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
| | - Ching Eng Png
- Institute of High Performance Computing, Agency for Science, Technology, and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
| | - Wan-Li Yang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
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Singh V, Singh S, Abah O, Müstecaplıoğlu ÖE. Unified trade-off optimization of quantum harmonic Otto engine and refrigerator. Phys Rev E 2022; 106:024137. [PMID: 36110016 DOI: 10.1103/physreve.106.024137] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2022] [Accepted: 08/09/2022] [Indexed: 06/15/2023]
Abstract
We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum Ω function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.
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Affiliation(s)
- Varinder Singh
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Satnam Singh
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, Sector 81, S.A.S. Nagar, Manauli PO 140306, Punjab, India
| | - Obinna Abah
- Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
- School of Mathematics, Statistics, and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Özgür E Müstecaplıoğlu
- Department of Physics, Koç University, 34450 Sarıyer, Istanbul, Turkey
- TÜBÍTAK Research Institute for Fundamental Sciences, 41470 Gebze, Turkey
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Unravelling the non-classicality role in Gaussian heat engines. Sci Rep 2022; 12:10412. [PMID: 35729309 PMCID: PMC9213435 DOI: 10.1038/s41598-022-13811-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 05/27/2022] [Indexed: 11/08/2022] Open
Abstract
At the heart of quantum thermodynamics lies a fundamental question about what is genuine "quantum" in quantum heat engines and how to seek this quantumness, so that thermodynamical tasks could be performed more efficiently compared with classical protocols. Here, using the concept of P-representability, we define a function called classicality, which quantifies the degree of non-classicality of bosonic modes. This function allows us to explore the role of non-classicality in quantum heat engines and design optimal protocols for work extraction. For two specific cycles, a quantum Otto and a generalised one, we show that non-classicality is a fundamental resource for performing thermodynamic tasks more efficiently.
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Arısoy O, Hsiang JT, Hu BL. Quantum-parametric-oscillator heat engines in squeezed thermal baths: Foundational theoretical issues. Phys Rev E 2022; 105:014108. [PMID: 35193212 DOI: 10.1103/physreve.105.014108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Accepted: 12/21/2021] [Indexed: 06/14/2023]
Abstract
In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of four stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact non-Markovian equation which preserves the positivity of the density operator and is valid for (1) all temperatures, (2) arbitrary spectral density of the bath, and (3) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This includes (1) the non-Markovian regimes for non-Ohmic, low-temperature baths, (2) what to expect in nonadiabatic frequency modulations, (3) strong system-bath coupling, as well as (4) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces that we hope are of use for exploring such possibilities.
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Affiliation(s)
- Onat Arısoy
- Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Jen-Tsung Hsiang
- Center for High Energy and High Field Physics, National Central University, Taoyuan 320317, Taiwan, ROC
| | - Bei-Lok Hu
- Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA
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Lin J, Li K, He J, Ren J, Wang J. Power statistics of Otto heat engines with the Mpemba effect. Phys Rev E 2022; 105:014104. [PMID: 35193214 DOI: 10.1103/physreve.105.014104] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 12/14/2021] [Indexed: 01/13/2023]
Abstract
The Mpemba effect is a counterintuitive relaxation phenomenon whereby a system with a higher initial temperature may cool down to the thermal state faster than an identical system that was initially prepared at a lower temperature. Here, we investigate heat and work in a Markovian state transition system with cyclic switching hot-cold temperatures, which operates as an Otto heat engine working in long but finite time, either with or without the Mpemba effect. Under the condition of the periodic steady state having been reached, the time durations of the heating and cooling relaxation processes are determined by exploring a distance-from-equilibrium equivalent to the Kullback-Leibler divergence. We then numerically evaluate and compare the averages and variances of both the work and the power output of two scenarios with and without the Mpemba effect. The results show that the Markovian Mpemba effect can enhance the machine performance by significantly increasing the power output for a given efficiency without sacrificing the stability.
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Affiliation(s)
- Jie Lin
- 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
| | - 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 Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China.,State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
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