1
|
Pei JH, Chen JF, Quan HT. Exploring quasiprobability approaches to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution. Phys Rev E 2023; 108:054109. [PMID: 38115414 DOI: 10.1103/physreve.108.054109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 10/09/2023] [Indexed: 12/21/2023]
Abstract
In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.
Collapse
Affiliation(s)
- Ji-Hui Pei
- School of Physics, Peking University, Beijing 100871, China
| | - 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
| |
Collapse
|
2
|
Erdman PA, Noé F. Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning. PNAS NEXUS 2023; 2:pgad248. [PMID: 37593201 PMCID: PMC10427747 DOI: 10.1093/pnasnexus/pgad248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 07/13/2023] [Accepted: 07/25/2023] [Indexed: 08/19/2023]
Abstract
A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on reinforcement learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal tradeoffs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.
Collapse
Affiliation(s)
- Paolo A Erdman
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Microsoft Research AI4Science, Karl-Liebknecht Str. 32, 10178 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, TX 77005, USA
| |
Collapse
|
3
|
Peña FJ, Myers NM, Órdenes D, Albarrán-Arriagada F, Vargas P. Enhanced Efficiency at Maximum Power in a Fock-Darwin Model Quantum Dot Engine. ENTROPY (BASEL, SWITZERLAND) 2023; 25:518. [PMID: 36981406 PMCID: PMC10047958 DOI: 10.3390/e25030518] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 03/15/2023] [Accepted: 03/15/2023] [Indexed: 06/18/2023]
Abstract
We study the performance of an endoreversible magnetic Otto cycle with a working substance composed of a single quantum dot described using the well-known Fock-Darwin model. We find that tuning the intensity of the parabolic trap (geometrical confinement) impacts the proposed cycle's performance, quantified by the power, work, efficiency, and parameter region where the cycle operates as an engine. We demonstrate that a parameter region exists where the efficiency at maximum output power exceeds the Curzon-Ahlborn efficiency, the efficiency at maximum power achieved by a classical working substance.
Collapse
Affiliation(s)
- Francisco J. Peña
- Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 11520, Chile
- Millennium Nucleus in NanoBioPhysics (NNBP), Av. España 1680, Valparaíso 11520, Chile
| | - Nathan M. Myers
- Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA
| | - Daniel Órdenes
- Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 11520, Chile
- Millennium Nucleus in NanoBioPhysics (NNBP), Av. España 1680, Valparaíso 11520, Chile
| | - Francisco Albarrán-Arriagada
- Departamento de Física, CEDENNA, Universidad de Santiago de Chile (USACH), Avenida Víctor Jara 3493, Estación Central 9170124, Chile
| | - Patricio Vargas
- Departamento de Física, CEDENNA, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 11520, Chile
| |
Collapse
|
4
|
Soriani A, Miranda E, Deffner S, Bonança MVS. Shortcuts to Thermodynamic Quasistaticity. PHYSICAL REVIEW LETTERS 2022; 129:170602. [PMID: 36332265 DOI: 10.1103/physrevlett.129.170602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 09/16/2022] [Accepted: 09/22/2022] [Indexed: 06/16/2023]
Abstract
The operation of near-term quantum technologies requires the development of feasible, implementable, and robust strategies of controlling complex many body systems. To this end, a variety of techniques, so-called "shortcuts to adiabaticity," have been developed. Many of these shortcuts have already been demonstrated to be powerful and implementable in distinct scenarios. Yet, it is often also desirable to have additional, approximate strategies available that are applicable to a large class of systems. Hence, in this Letter, we take inspiration from thermodynamics and propose to focus on the macrostate, rather than the microstate. Adiabatic dynamics can then be identified as such processes that preserve the equation of state, and systematic corrections are obtained from adiabatic perturbation theory. We demonstrate this approach by improving upon fast quasiadiabatic driving, and by applying the method to the quantum Ising chain in the transverse field.
Collapse
Affiliation(s)
- Artur Soriani
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
| | - Eduardo Miranda
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Marcus V S Bonança
- Gleb Wataghin Institute of Physics, University of Campinas, Campinas, São Paulo 13083-950, Brazil
| |
Collapse
|
5
|
Shastri R, Venkatesh BP. Optimization of asymmetric quantum Otto engine cycles. Phys Rev E 2022; 106:024123. [PMID: 36109960 DOI: 10.1103/physreve.106.024123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 08/02/2022] [Indexed: 06/15/2023]
Abstract
We consider the optimization of the work output and fluctuations of a finite-time quantum Otto heat engine cycle consisting of compression and expansion work strokes of unequal duration. The asymmetry of the cycle is characterized by a parameter r_{u} giving the ratio of the times for the compression and expansion work strokes. For such an asymmetric quantum Otto engine cycle, with working substance chosen as a harmonic oscillator or a two-level system, we find that the optimal values of r_{u} maximizing the work output and the reliability (defined as the ratio of average work output to its standard deviation) shows discontinuities as a function of the total time taken for the cycle. Moreover we identify cycles of some specific duration where both the work output and the reliability take their largest values for the same value of the asymmetry parameter r_{u}.
Collapse
Affiliation(s)
- Rahul Shastri
- Indian Institute of Technology Gandhinagar, Palaj, Gujarat 382355, India
| | | |
Collapse
|
6
|
Cherubim C, de Oliveira TR, Jonathan D. Nonadiabatic coupled-qubit Otto cycle with bidirectional operation and efficiency gains. Phys Rev E 2022; 105:044120. [PMID: 35590646 DOI: 10.1103/physreve.105.044120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 03/28/2022] [Indexed: 06/15/2023]
Abstract
We study a quantum Otto cycle that uses a 2-qubit working substance whose Hamiltonian does not commute with itself at different times during unitary strokes. We investigate how the cycle responds to the loss of quantum adiabaticity when these strokes are operated with a finite duration. We find that qualitative features such as the possibility of counter-rotating cycles operating as heat engines, or a cycle efficiency that can increase with a decrease in the temperature difference between the baths, are resilient even to highly nonadiabatic strokes. However, cycle efficiency rapidly decreases, although it can still remain above the standard Otto value for small degrees of quantum nonadiabaticity.
Collapse
Affiliation(s)
- Cleverson Cherubim
- Instituto de Física, Universidade Federal Fluminense, Gragoatá 24210-346, Niterói, RJ, Brazil
| | - Thiago R de Oliveira
- Instituto de Física, Universidade Federal Fluminense, Gragoatá 24210-346, Niterói, RJ, Brazil
| | - Daniel Jonathan
- Instituto de Física, Universidade Federal Fluminense, Gragoatá 24210-346, Niterói, RJ, Brazil
| |
Collapse
|
7
|
Chand S, Dasgupta S, Biswas A. Finite-time performance of a single-ion quantum Otto engine. Phys Rev E 2021; 103:032144. [PMID: 33862721 DOI: 10.1103/physreve.103.032144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.
Collapse
Affiliation(s)
- Suman Chand
- Department of Physics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India
| | - Shubhrangshu Dasgupta
- Department of Physics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India
| | - Asoka Biswas
- Department of Physics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India
| |
Collapse
|
8
|
Ma YH. Effect of Finite-Size Heat Source's Heat Capacity on the Efficiency of Heat Engine. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1002. [PMID: 33286771 PMCID: PMC7597076 DOI: 10.3390/e22091002] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Revised: 09/02/2020] [Accepted: 09/07/2020] [Indexed: 11/20/2022]
Abstract
Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper, we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature difference. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We firstly investigate the effects of different heat capacity characteristics of the sources on the heat engine's efficiency at maximum work (EMW) in the quasi-static limit. Moreover, it is found that the efficiency of the engine operating in finite-time with maximum power of each cycle is achieved follows a simple universality as η=ηC/4+OηC2, where ηC is the Carnot efficiency determined by the initial temperature of the sources. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be ηMW=2-2.
Collapse
Affiliation(s)
- Yu-Han Ma
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China;
- Beijing Computational Science Research Center, Beijing 100193, China
| |
Collapse
|
9
|
Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit. ENTROPY 2020; 22:e22040457. [PMID: 33286231 PMCID: PMC7516941 DOI: 10.3390/e22040457] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Revised: 04/15/2020] [Accepted: 04/16/2020] [Indexed: 11/22/2022]
Abstract
At the classical limit, a multi-stage, endoreversible Carnot cycle model of quantum heat engine (QHE) working with non-interacting harmonic oscillators systems is established in this paper. A simplified combined cycle, where all sub-cycles work at maximum power output (MPO), is analyzed under two types of combined form: constraint of cycle period or constraint of interstage heat current. The expressions of power and the corresponding efficiency under two types of combined constrains are derived. A general combined cycle, in which all sub-cycles run at arbitrary state, is further investigated under two types of combined constrains. By introducing the Lagrangian function, the MPO of two-stage combined QHE with different intermediate temperatures is obtained, utilizing numerical calculation. The results show that, for the simplified combined cycle, the total power decreases and heat exchange from hot reservoir increases under two types of constrains with the increasing number (N) of stages. The efficiency of the combined cycle decreases under the constraints of the cycle period, but keeps constant under the constraint of interstage heat current. For the general combined cycle, three operating modes, including single heat engine mode at low “temperature” (SM1), double heat engine mode (DM) and single heat engine mode at high “temperature” (SM2), appear as intermediate temperature varies. For the constraint of cycle period, the MPO is obtained at the junction of DM mode and SM2 mode. For the constraint of interstage heat current, the MPO keeps constant during DM mode, in which the two sub-cycles compensate each other.
Collapse
|
10
|
Lee S, Ha M, Park JM, Jeong H. Finite-time quantum Otto engine: Surpassing the quasistatic efficiency due to friction. Phys Rev E 2020; 101:022127. [PMID: 32168587 DOI: 10.1103/physreve.101.022127] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2019] [Accepted: 02/04/2020] [Indexed: 06/10/2023]
Abstract
In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called "friction." To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that, even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does.
Collapse
Affiliation(s)
- Sangyun Lee
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34051, Korea
| | - Meesoon Ha
- Department of Physics Education, Chosun University, Gwangju 61452, Korea
| | - Jong-Min Park
- School of Physics, Korea Institute for Advanced Study, Seoul, 02455, Korea
| | - Hawoong Jeong
- Department of Physics and Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| |
Collapse
|
11
|
Chen JF, Sun CP, Dong H. Achieve higher efficiency at maximum power with finite-time quantum Otto cycle. Phys Rev E 2020; 100:062140. [PMID: 31962481 DOI: 10.1103/physreve.100.062140] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Indexed: 11/07/2022]
Abstract
The optimization of heat engines was intensively explored to achieve higher efficiency while maintaining the output power. However, most investigations were limited to a few finite-time cycles, e.g., the Carnot-like cycle, due to the complexity of the finite-time thermodynamics. In this paper, we propose a class of finite-time engine with quantum Otto cycle, and demonstrate a higher achievable efficiency at maximum power. The current model can be widely utilized, benefitting from the general C/τ^{2} scaling of extra work for a finite-time adiabatic process with long control time τ. We apply the adiabatic perturbation method to the quantum piston model and calculate the efficiency at maximum power, which is validated with an exact solution.
Collapse
Affiliation(s)
- Jin-Fu Chen
- Beijing Computational Science Research Center, Beijing 100193, China.,Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Chang-Pu Sun
- Beijing Computational Science Research Center, Beijing 100193, China.,Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| | - Hui Dong
- Graduate School of China Academy of Engineering Physics, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China
| |
Collapse
|