1
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Koyanagi S, Tanimura Y. Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle. J Chem Phys 2024; 160:234112. [PMID: 38904216 DOI: 10.1063/5.0205771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2024] [Accepted: 05/23/2024] [Indexed: 06/22/2024] Open
Abstract
We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system-bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu-Planck potentials as entropic potentials and the Helmholtz-Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker-Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system-bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions.
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Affiliation(s)
- Shoki Koyanagi
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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2
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Arrachea L. Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:036501. [PMID: 36603220 DOI: 10.1088/1361-6633/acb06b] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 01/05/2023] [Indexed: 06/17/2023]
Abstract
We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.
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Affiliation(s)
- Liliana Arrachea
- Escuela de Ciencia y Tecnología and ICIFI, Universidad de San Martín, Av. 25 de Mayo y Francia, 1650 Buenos Aires, Argentina
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3
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Ochoa MA. Quantum thermodynamics of periodically driven polaritonic systems. Phys Rev E 2022; 106:064113. [PMID: 36671137 DOI: 10.1103/physreve.106.064113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 11/16/2022] [Indexed: 06/17/2023]
Abstract
We investigate the energy distribution and quantum thermodynamics in periodically-driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and quantify the energy reorganization between these two systems and their interaction as a function of coupling strength, driving force, and detuning. After deriving the quantum master equation for the polariton density matrix with weak environment interactions, we obtain the dissipative time propagator and the long-time evolution of an equilibrium initial state. This approach provides direct access to the stationary state and overcomes the difficulties found in the numerical evolution of weakly damped quantum systems near resonance, also providing maps on the polariton lineshape. Then, we compute the thermodynamic performance during harmonic modulation and demonstrate that maximum efficiency occurs at resonance. We also provide an expression for the irreversible heat rate and numerically demonstrate that this agrees with the thermodynamic laws.
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Affiliation(s)
- Maicol A Ochoa
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland, USA
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4
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Tong K, Dou W. Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: non-equilibrium entropy production and higher order corrections. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:495703. [PMID: 36223783 DOI: 10.1088/1361-648x/ac99c8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 10/12/2022] [Indexed: 06/16/2023]
Abstract
We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Douet al2020Phys. Rev.B101184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Douet al(2020Phys. Rev.B101184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.
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Affiliation(s)
- Kaiyi Tong
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
| | - Wenjie Dou
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
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5
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Koyanagi S, Tanimura Y. Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams. J Chem Phys 2022; 157:084110. [DOI: 10.1063/5.0107305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the system--bath (SB) interactions controlling the transition between these processes. Numerical simulations are conducted in a nonperturbative and non-Markovian SB coupling regime using the hierarchical equations of motion under these fields at different cycle frequencies. The work applied to the total system and the heat exchanged with the baths are rigorously evaluated. In addition, by regarding quasi-static work as free energy, we compute the quantum thermodynamic variables and analyze the simulation results using thermodynamic work diagrams for the first time. Analysis of these diagrams indicates that, in the strong SB coupling region, the fields for the SB interactions are major sources of work, while in other regions, the field for the subsystem is a source of work. We find that the maximum efficiency is achieved in the quasi-static case and is determined solely by the bath temperatures, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.
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6
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Dattagupta S. Energy conductance across a mesoscopic junction in a nonequilibrium spin-boson model under the influence of telegraph noise. Phys Rev E 2022; 105:044128. [PMID: 35590635 DOI: 10.1103/physreve.105.044128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 04/04/2022] [Indexed: 06/15/2023]
Abstract
A spin-boson model in the presence of a telegraph noise (TN) source is employed to calculate the energy conductance between a tunnel junction and two bosonic baths. A polaron-transformed coupling term with the bosonic baths allows for treating quantum damping to arbitrary orders of strength. However, the polaron transformation yields a dressed tunneling frequency which is assumed small and treated perturbatively as is familiar in the noninteracting blip approximation in the context of the nonequilibrium spin-boson model. While the coupling with the bosonic baths leads to decoherence in an otherwise coherent tunneling process, the TN induces a different kind of fluctuation, that is, in the asymmetry of the underlying two-level system. It is the interplay of these two different relaxation effects, one triggered by the two quantum (bosonic) baths and the other through a classical bath (creating a TN), that is investigated here in detail. The TN that mimics the classical, fluctuating environment makes a nontrivial contribution to the self-energy that helps compute the imaginary part of the spin susceptibility which, in turn, determines the energy transfer across the junction. The range of validity of the TN is clarified at the outset and its efficacy in tuning the environmental influence is pointed out. The present paper complements an earlier similar study-albeit for fermionic baths-and provides additional input in terms of the TN to a previous investigation of energy transfer between a nanojunction and bosonic reservoirs without, however, the noisy environment.
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7
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Chen JF, Qiu T, Quan HT. Quantum-Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1602. [PMID: 34945908 PMCID: PMC8700725 DOI: 10.3390/e23121602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Revised: 11/22/2021] [Accepted: 11/23/2021] [Indexed: 11/17/2022]
Abstract
Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.
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Affiliation(s)
- Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
| | - Tian Qiu
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
| | - Hai-Tao Quan
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, China
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8
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Liu J, Jung KA, Segal D. Periodically Driven Quantum Thermal Machines from Warming up to Limit Cycle. PHYSICAL REVIEW LETTERS 2021; 127:200602. [PMID: 34860071 DOI: 10.1103/physrevlett.127.200602] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 10/15/2021] [Indexed: 06/13/2023]
Abstract
Theoretical treatments of periodically driven quantum thermal machines (PD-QTMs) are largely focused on the limit-cycle stage of operation characterized by a periodic state of the system. Yet, this regime is not immediately accessible for experimental verification. Here, we present a general thermodynamic framework that handles the performance of PD-QTMs both before and during the limit-cycle stage of operation. It is achieved by observing that periodicity may break down at the ensemble average level, even in the limit-cycle phase. With this observation, and using conventional thermodynamic expressions for work and heat, we find that a complete description of the first law of thermodynamics for PD-QTMs requires a new contribution, which vanishes only in the limit-cycle phase under rather weak system-bath couplings. Significantly, this contribution is substantial at strong couplings even at limit cycle, thus largely affecting the behavior of the thermodynamic efficiency. We demonstrate our framework by simulating a quantum Otto engine building upon a driven resonant level model. Our results provide new insights towards a complete description of PD-QTMs, from turn-on to the limit-cycle stage and, particularly, shed light on the development of quantum thermodynamics at strong coupling.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Kenneth A Jung
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
- Department of Physics, 60 Saint George St., University of Toronto, Toronto, Ontario M5S 1A7, Canada
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9
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Candeloro A, Razzoli L, Bordone P, Paris MGA. Role of topology in determining the precision of a finite thermometer. Phys Rev E 2021; 104:014136. [PMID: 34412220 DOI: 10.1103/physreve.104.014136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2021] [Accepted: 07/07/2021] [Indexed: 12/17/2022]
Abstract
Temperature fluctuations of a finite system follow the Landau bound δT^{2}=T^{2}/C(T) where C(T) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
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Affiliation(s)
- Alessandro Candeloro
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133 Milan, Italy
| | - Luca Razzoli
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy
| | - Paolo Bordone
- Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, I-41125 Modena, Italy.,Centro S3, CNR-Istituto di Nanoscienze, I-41125 Modena, Italy
| | - Matteo G A Paris
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133 Milan, Italy.,INFN, Sezione di Milano, I-20133 Milan, Italy
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10
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Gu L, Wu R. Density functional study of relaxation of adsorbate vibration modes: Dominance of anharmonic interaction. J Chem Phys 2020; 153:184109. [PMID: 33187426 DOI: 10.1063/5.0027915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Formulation and density functional workflow for calculating the lifetime of vibrational modes of molecular adsorbates on solid surfaces due to vibration-phonon coupling are presented. The anharmonic coupling is invoked to give the correct description of the origin of temperature dependence. Using pyrrolidine (C4H9N) absorbed on the Cu(001) surface as a concrete example, we show that the anharmonic coupling can be one to two orders more significant than the harmonic interaction for the broadening of vibrational spectra, especially as temperature increases. These results challenge the common assumption that the anharmonic interaction is weak and call for attention of considering its effect in quantum relaxation and related problems.
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Affiliation(s)
- Lei Gu
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - Ruqian Wu
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
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11
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Ali MM, Huang WM, Zhang WM. Quantum thermodynamics of single particle systems. Sci Rep 2020; 10:13500. [PMID: 32782281 PMCID: PMC7419543 DOI: 10.1038/s41598-020-70450-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2020] [Accepted: 06/30/2020] [Indexed: 11/24/2022] Open
Abstract
Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved.
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Affiliation(s)
- Md Manirul Ali
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Wei-Ming Huang
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Wei-Min Zhang
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan.
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12
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Semenov A, Nitzan A. Transport and thermodynamics in quantum junctions: A scattering approach. J Chem Phys 2020; 152:244126. [PMID: 32610981 DOI: 10.1063/5.0010127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for quantum transport and reproduces recently obtained results for the quantum thermodynamics of slowly driven systems. Using this approach, new results have been obtained. First, we derived a general explicit expression for the non-equilibrium steady-state density matrix of a system composed of multiple infinite baths coupled through a general interaction. Then, we obtained a general expression for the dissipated power for the driven non-interacting resonant level to the first order in the driving speeds, where both the dot energy level and its couplings are changing, without invoking the wide-band approximation. In addition, we also showed that the symmetric splitting of the system bath interaction, employed for the case of a system coupled to one bath to determine the effective system Hamiltonian [A. Bruch et al., Phys. Rev. B 93, 115318 (2016)], is valid for the multiple bath case as well. Finally, we demonstrated an equivalence of our method to the Landauer-Buttiker formalism and its extension to slowly driven systems developed by Bruch, Lewenkopf, and von Oppen [Phys. Rev. Lett. 120, 107701 (2018)]. To demonstrate the use of this formalism, we analyze the operation of a device in which the dot is driven cyclically between two leads under strong coupling conditions. We also generalize the previously obtained expression for entropy production in such driven processes to the many-bath case.
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Affiliation(s)
- Alexander Semenov
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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13
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Duan C, Hsieh CY, Liu J, Wu J, Cao J. Unusual Transport Properties with Noncommutative System-Bath Coupling Operators. J Phys Chem Lett 2020; 11:4080-4085. [PMID: 32354212 DOI: 10.1021/acs.jpclett.0c00985] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Understanding nonequilibrium transport is crucial for controlling energy flow in nanoscale systems. We study thermal energy transfer in a generalized nonequilibrium spin-boson model (NESB) with noncommutative system-bath coupling operators and discover its unusual transport properties. Compared to the conventional NESB, the energy current is greatly enhanced by rotating the system-bath coupling operators. Constructive contribution to thermal rectification can be optimized when two sources of asymmetry, system-bath coupling strength and coupling operators, coexist. At the weak coupling and the adiabatic limit, the scaling dependence of energy current on the coupling strength and the system energy gap changes drastically when the coupling operators become noncommutative. These scaling relations can further be explained analytically by the nonequilibrium polaron-transformed Redfield equation (NE-PTRE). These novel transport properties, arising from the pure quantum effect of noncommutative coupling operators, suggest an unvisited dimension of controlling transport in nanoscale systems and should generally appear in other nonequilibrium set-ups and driven systems.
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Affiliation(s)
- Chenru Duan
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Chang-Yu Hsieh
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
| | - Junjie Liu
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
| | - Jianlan Wu
- Physics Department, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
- Singapore-MIT Alliance for Research and Technology (SMART) Center, Singapore 138602
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14
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Strasberg P, Esposito M. Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force. Phys Rev E 2020; 101:050101. [PMID: 32575212 DOI: 10.1103/physreve.101.050101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 04/22/2020] [Indexed: 11/07/2022]
Abstract
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we refute a key criticism expressed in the works by P. Talkner and P. Hänggi [Phys. Rev. E 94, 022143 (2016)10.1103/PhysRevE.94.022143 and arXiv:1911.11660]. We also discuss the remaining part of the criticism.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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15
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Zimbovskaya NA, Nitzan A. Energy, Work, Entropy, and Heat Balance in Marcus Molecular Junctions. J Phys Chem B 2020; 124:2632-2642. [PMID: 32163712 DOI: 10.1021/acs.jpcb.0c00059] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a consistent theory of energy balance and conversion in a single-molecule junction with strong interactions between electrons on the molecular linker (dot) and phonons in the nuclear environment where the Marcus-type electron hopping processes predominate in the electron transport. It is shown that the environmental reorganization and relaxation that accompany electron hopping energy exchange between the electrodes and the nuclear (molecular and solvent) environment may bring a moderate local cooling of the latter in biased systems. The effect of a periodically driven dot level on the heat transport and power generated in the system is analyzed, and energy conservation is demonstrated both within and beyond the quasistatic regime. Finally, a simple model of atomic scale engine based on a Marcus single-molecule junction with a driven electron level is suggested and discussed.
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Affiliation(s)
- Natalya A Zimbovskaya
- Department of Physics and Electronics, University of Puerto Rico-Humacao, CUH Station, Humacao, Puerto Rico 00791, United States
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States.,School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
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16
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Kwon C, Um J, Yeo J, Park H. Three heats in a strongly coupled system and bath. Phys Rev E 2019; 100:052127. [PMID: 31869951 DOI: 10.1103/physreve.100.052127] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2018] [Indexed: 11/07/2022]
Abstract
We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat, Q_{S} and Q_{B}, from the energy loss of the system and the energy gain of the bath, respectively. This is in contrast to the equivalence of Q_{S} and Q_{B}, which is commonly assumed to hold in the weak-coupling regime. The bath we consider is equipped with a thermostat which enables it to reach an equilibrium. We identify another kind of heat Q_{SB} from the energy dissipation of the bath into the superbath that provides the thermostat. We derive the fluctuation theorems (FTs) for the system variables and various heats, which are discussed in comparison with the FT for the total entropy production. We take an example of a sliding harmonic potential of a single Brownian particle in a fluid and calculate the three heats in a simplified model. These heats are found to equal, on average, in the steady state of energy, but show different fluctuations at all times.
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Affiliation(s)
- Chulan Kwon
- Department of Physics, Myongji University, Yongin, Gyeonggi-Do 17058, Korea
| | - Jaegon Um
- BK21PLUS Physics Division, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Joonhyun Yeo
- Department of Physics, Konkuk University, Seoul 05029, Korea
| | - Hyunggyu Park
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
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17
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Oz A, Hod O, Nitzan A. Numerical Approach to Nonequilibrium Quantum Thermodynamics: Nonperturbative Treatment of the Driven Resonant Level Model Based on the Driven Liouville von-Neumann Formalism. J Chem Theory Comput 2019; 16:1232-1248. [DOI: 10.1021/acs.jctc.9b00999] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19103, United States
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18
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Strasberg P. Repeated Interactions and Quantum Stochastic Thermodynamics at Strong Coupling. PHYSICAL REVIEW LETTERS 2019; 123:180604. [PMID: 31763881 DOI: 10.1103/physrevlett.123.180604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Indexed: 06/10/2023]
Abstract
The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings, the theory is then extended to arbitrary measurements performed on the system. This constitutes a direct experimentally testable framework in strong coupling quantum thermodynamics. By construction, it provides many quantum stochastic processes and quantum causal models with a consistent thermodynamic interpretation. The setting can be further used, for instance, to rigorously investigate the interplay between non-Markovianity and nonequilibrium thermodynamics.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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19
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Bustos-Marún RA, Calvo HL. Thermodynamics and Steady State of Quantum Motors and Pumps Far from Equilibrium. ENTROPY 2019. [PMCID: PMC7515353 DOI: 10.3390/e21090824] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
In this article, we briefly review the dynamical and thermodynamical aspects of different forms of quantum motors and quantum pumps. We then extend previous results to provide new theoretical tools for a systematic study of those phenomena at far-from-equilibrium conditions. We mainly focus on two key topics: (1) The steady-state regime of quantum motors and pumps, paying particular attention to the role of higher order terms in the nonadiabatic expansion of the current-induced forces. (2) The thermodynamical properties of such systems, emphasizing systematic ways of studying the relationship between different energy fluxes (charge and heat currents and mechanical power) passing through the system when beyond-first-order expansions are required. We derive a general order-by-order scheme based on energy conservation to rationalize how every order of the expansion of one form of energy flux is connected with the others. We use this approach to give a physical interpretation of the leading terms of the expansion. Finally, we illustrate the above-discussed topics in a double quantum dot within the Coulomb-blockade regime and capacitively coupled to a mechanical rotor. We find many exciting features of this system for arbitrary nonequilibrium conditions: a definite parity of the expansion coefficients with respect to the voltage or temperature biases; negative friction coefficients; and the fact that, under fixed parameters, the device can exhibit multiple steady states where it may operate as a quantum motor or as a quantum pump, depending on the initial conditions.
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Affiliation(s)
- Raúl A. Bustos-Marún
- Instituto de Física Enrique Gaviola (CONICET) and FaMAF, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
- Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
- Correspondence: (R.A.B.-M.); (H.L.C.)
| | - Hernán L. Calvo
- Instituto de Física Enrique Gaviola (CONICET) and FaMAF, Universidad Nacional de Córdoba, Córdoba 5000, Argentina
- Departamento de Física, Universidad Nacional de Río Cuarto, Ruta 36, Km 601, Río Cuarto 5800, Argentina
- Correspondence: (R.A.B.-M.); (H.L.C.)
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20
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Wei W, Huang B, Dai Y. Photoexcited charge carrier behaviors in solar energy conversion systems from theoretical simulations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1441] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Wei Wei
- School of Physics, State Key Laboratory of Crystal Materials Shandong University Jinan China
| | - Baibiao Huang
- School of Physics, State Key Laboratory of Crystal Materials Shandong University Jinan China
| | - Ying Dai
- School of Physics, State Key Laboratory of Crystal Materials Shandong University Jinan China
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21
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Jin Z, Subotnik JE. A practical ansatz for evaluating the electronic friction tensor accurately, efficiently, and in a nearly black-box format. J Chem Phys 2019; 150:164105. [PMID: 31042890 DOI: 10.1063/1.5085683] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is well-known that under conditions of fast electronic equilibration and weak nonadiabaticity, nonadiabatic effects induced by electron-hole pair excitations can be partly incorporated through a frictional force. However, ab initio computation of the electronic friction tensor suffers from numerical instability and usually demands a convergence check. In this study, we present an efficient and accurate interpolation method for computing the electronic friction tensor in a nearly black-box manner as appropriate for molecular dynamics. In almost all cases, our method agrees quite well with the exact friction tensor which is available for several quadratic Hamiltonians. As such, we outperform more conventional approaches that are based on the introduction of a broadening parameter. Future work will implement this interpolation approach within ab initio software packages.
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Affiliation(s)
- Zuxin Jin
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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22
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Kato A, Tanimura Y. Hierarchical Equations of Motion Approach to Quantum Thermodynamics. ACTA ACUST UNITED AC 2019. [DOI: 10.1007/978-3-319-99046-0_24] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
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23
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Thingna J, Esposito M, Barra F. Landau-Zener Lindblad equation and work extraction from coherences. Phys Rev E 2019; 99:042142. [PMID: 31108683 DOI: 10.1103/physreve.99.042142] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Indexed: 06/09/2023]
Abstract
We show that the dynamics of a driven quantum system weakly coupled to a finite reservoir can be approximated by a sequence of Landau-Zener transitions if the level spacing of the reservoir is large enough. This approximation can be formulated as a repeated interaction dynamics and leads to a quantum master equation for the driven system which is of Lindblad form. The approach is validated by comparison with the numerically exact full system dynamics. To emphasize the role of coherence in the master equation, we propose a model system which shows that in its presence, work can be extracted from a thermal reservoir while if the coherences vanish, then no work can be extracted.
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Affiliation(s)
- Juzar Thingna
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 Santa Barbara, USA
| | - Felipe Barra
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 Santa Barbara, USA
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
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24
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Oz I, Hod O, Nitzan A. Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1584338] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Inbal Oz
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
| | - Abraham Nitzan
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IL, Israel
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, IL, Israel
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA, USA
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25
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Strasberg P, Esposito M. Non-Markovianity and negative entropy production rates. Phys Rev E 2019; 99:012120. [PMID: 30780330 DOI: 10.1103/physreve.99.012120] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Indexed: 11/07/2022]
Abstract
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.
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Affiliation(s)
- Philipp Strasberg
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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26
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Miao G, Ouyang W, Subotnik J. A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping. J Chem Phys 2019; 150:041711. [PMID: 30709317 DOI: 10.1063/1.5050235] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within a generalized Anderson-Holstein model, we investigate electron transfer rates using two different surface hopping algorithms: a broadened classical master equation (BCME) and independent electron surface hopping (IESH). We find that for large enough bandwidth and density of one electron states, and in the presence of external friction, the IESH results converge to the BCME results for impurity-bath model systems, recovering both relaxation rates and equilibrium populations. Without external friction, however, the BCME and IESH results can strongly disagree, and preliminary evidence suggests that IESH does not always recover the correct equilibrium state. Finally, we also demonstrate that adding an electronic thermostat to IESH does help drive the metallic substrate to the correct equilibrium state, but this improvement can sometimes come at the cost of worse short time dynamics. Overall, our results should be of use for all computational chemists looking to model either gas phase scattering or electrochemical dynamics at a metal interface.
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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27
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Abstract
This paper presents a viewpoint on natural philosophy focusing on the organization of substance, as well as its changes as invited by the Second Law of thermodynamics. Modes of change are pointed to as definitive of levels of organization; these include physical, chemical, and biological modes of change. Conceptual uses of the subsumptive hierarchy format are employed throughout this paper. Developmental change in dissipative structures is examined in some detail, generating an argument for the use of final causality in studies of natural systems. Considerations of ‘internalism’ in science are presented along the way.
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28
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Liu J, Hsieh CY, Wu C, Cao J. Frequency-dependent current noise in quantum heat transfer: A unified polaron calculation. J Chem Phys 2018; 148:234104. [PMID: 29935498 DOI: 10.1063/1.5025367] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.
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Affiliation(s)
- Junjie Liu
- Singapore-MIT Alliance for Research and Technology (SMART) Center, 1 CREATE Way, Singapore 138602, Singapore
| | - Chang-Yu Hsieh
- Singapore-MIT Alliance for Research and Technology (SMART) Center, 1 CREATE Way, Singapore 138602, Singapore
| | - Changqin Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jianshu Cao
- Singapore-MIT Alliance for Research and Technology (SMART) Center, 1 CREATE Way, Singapore 138602, Singapore
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29
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Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations. ENTROPY 2018; 20:e20060423. [PMID: 33265513 PMCID: PMC7512941 DOI: 10.3390/e20060423] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Revised: 05/28/2018] [Accepted: 05/30/2018] [Indexed: 11/17/2022]
Abstract
Identifying or constructing a fine-grained microscopic theory that will emerge under specific conditions to a known macroscopic theory is always a formidable challenge. Thermodynamics is perhaps one of the most powerful theories and best understood examples of emergence in physical sciences, which can be used for understanding the characteristics and mechanisms of emergent processes, both in terms of emergent structures and the emergent laws governing the effective or collective variables. Viewing quantum mechanics as an emergent theory requires a better understanding of all this. In this work we aim at a very modest goal, not quantum mechanics as thermodynamics, not yet, but the thermodynamics of quantum systems, or quantum thermodynamics. We will show why even with this minimal demand, there are many new issues which need be addressed and new rules formulated. The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior contains elements, such as quantum coherence, correlations, entanglement and fluctuations, that are not well recognized in traditional thermodynamics, built on large systems vanishingly weakly coupled to a non-dynamical reservoir. For quantum thermodynamics at strong coupling, one needs to reexamine the meaning of the thermodynamic functions, the viability of the thermodynamic relations and the validity of the thermodynamic laws anew. After a brief motivation, this paper starts with a short overview of the quantum formulation based on Gelin & Thoss and Seifert. We then provide a quantum formulation of Jarzynski's two representations. We show how to construct the operator thermodynamic potentials, the expectation values of which provide the familiar thermodynamic variables. Constructing the operator thermodynamic functions and verifying or modifying their relations is a necessary first step in the establishment of a viable thermodynamics theory for quantum systems. We mention noteworthy subtleties for quantum thermodynamics at strong coupling, such as in issues related to energy and entropy, and possible ambiguities of their operator forms. We end by indicating some fruitful pathways for further developments.
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30
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Perarnau-Llobet M, Wilming H, Riera A, Gallego R, Eisert J. Strong Coupling Corrections in Quantum Thermodynamics. PHYSICAL REVIEW LETTERS 2018; 120:120602. [PMID: 29694098 DOI: 10.1103/physrevlett.120.120602] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2017] [Revised: 12/19/2017] [Indexed: 06/08/2023]
Abstract
Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic non-Markovian quantum Brownian motion.
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Affiliation(s)
- M Perarnau-Llobet
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - H Wilming
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - A Riera
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - R Gallego
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - J Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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31
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Xu YY, Chen B, Liu J. Achieving the classical Carnot efficiency in a strongly coupled quantum heat engine. Phys Rev E 2018; 97:022130. [PMID: 29548214 DOI: 10.1103/physreve.97.022130] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Indexed: 11/07/2022]
Abstract
Generally, the efficiency of a heat engine strongly coupled with a heat bath is less than the classical Carnot efficiency. Through a model-independent method, we show that the classical Carnot efficiency is achieved in a strongly coupled quantum heat engine. First, we present the first law of quantum thermodynamics in strong coupling. Then, we show how to achieve the Carnot cycle and the classical Carnot efficiency at strong coupling. We find that this classical Carnot efficiency stems from the fact that the heat released in a nonequilibrium process is balanced by the absorbed heat. We also analyze the restrictions in the achievement of the Carnot cycle. The first restriction is that there must be two corresponding intervals of the controllable parameter in which the corresponding entropies of the work substance at the hot and cold temperatures are equal, and the second is that the entropy of the initial and final states in a nonequilibrium process must be equal. Through these restrictions, we obtain the positive work conditions, including the usual one in which the hot temperature should be higher than the cold, and a new one in which there must be an entropy interval at the hot temperature overlapping that at the cold. We demonstrate our result through a paradigmatic model-a two-level system in which a work substance strongly interacts with a heat bath. In this model, we find that the efficiency may abruptly decrease to zero due to the first restriction, and that the second restriction results in the control scheme becoming complex.
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Affiliation(s)
- Y Y Xu
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - B Chen
- Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
| | - J Liu
- Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
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32
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Bruch A, Lewenkopf C, von Oppen F. Landauer-Büttiker Approach to Strongly Coupled Quantum Thermodynamics: Inside-Outside Duality of Entropy Evolution. PHYSICAL REVIEW LETTERS 2018; 120:107701. [PMID: 29570311 DOI: 10.1103/physrevlett.120.107701] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Indexed: 06/08/2023]
Abstract
We develop a Landauer-Büttiker theory of entropy evolution in time-dependent, strongly coupled electron systems. The formalism naturally avoids the problem of the system-bath distinction by defining the entropy current in the attached leads. This current can then be used to infer changes of the entropy of the system which we refer to as the inside-outside duality. We carry out this program in an adiabatic expansion up to first order beyond the quasistatic limit. When combined with particle and energy currents, as well as the work required to change an external potential, our formalism provides a full thermodynamic description, applicable to arbitrary noninteracting electron systems in contact with reservoirs. This provides a clear understanding of the relation between heat and entropy currents generated by time-dependent potentials and their connection to the occurring dissipation.
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Affiliation(s)
- Anton Bruch
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Caio Lewenkopf
- Instituto de Física, Universidade Federal Fluminense, 24210-346 Niterói, Brazil
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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33
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Affiliation(s)
- Tie-jun Xiao
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, China
| | - Yun Zhou
- Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, China
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34
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Hsiang JT, Chou CH, Subaşı Y, Hu BL. Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law. Phys Rev E 2018; 97:012135. [PMID: 29448480 DOI: 10.1103/physreve.97.012135] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Indexed: 11/07/2022]
Abstract
In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.
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Affiliation(s)
- J-T Hsiang
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
| | - C H Chou
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
| | - Y Subaşı
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - B L Hu
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China.,Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
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35
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Tamascelli D, Smirne A, Huelga SF, Plenio MB. Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems. PHYSICAL REVIEW LETTERS 2018; 120:030402. [PMID: 29400486 DOI: 10.1103/physrevlett.120.030402] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Indexed: 06/07/2023]
Abstract
We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.
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Affiliation(s)
- D Tamascelli
- Università degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, I-20133 Milano, Italy
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - A Smirne
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - S F Huelga
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
| | - M B Plenio
- Institute of Theoretical Physics, Universität Ulm, Albert-Einstein-Allee 11D-89069 Ulm, Germany
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36
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Introduction to Quantum Thermodynamics: History and Prospects. FUNDAMENTAL THEORIES OF PHYSICS 2018. [DOI: 10.1007/978-3-319-99046-0_1] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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37
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Liu J, Xu H, Li B, Wu C. Energy transfer in the nonequilibrium spin-boson model: From weak to strong coupling. Phys Rev E 2017; 96:012135. [PMID: 29347139 DOI: 10.1103/physreve.96.012135] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Indexed: 06/07/2023]
Abstract
To explore energy transfer in the nonequilibrium spin-boson model (NESB) from weak to strong system-bath coupling regimes, we propose a polaron-transformed nonequilibrium Green's function (NEGF) method. By combining the polaron transformation, we are able to treat the system-bath coupling nonperturbatively, thus in direct contrast to conventionally used NEGF methods which take the system-bath coupling as a perturbation. The Majorana-fermion representation is further utilized to evaluate terms in the Dyson series. This method not only allows us to deal with weak as well as strong coupling regimes but also enables an investigation on the role of bias in the energy transfer. As an application of the method, we study an Ohmic NESB. For an unbiased spin system, our energy current result smoothly bridges predictions of two benchmarks, namely, the quantum master equation and the nonequilibrium noninteracting blip approximation, a considerable improvement over existing theories. In case of a biased spin system, we found a bias-induced nonmonotonic behavior of the energy conductance in the intermediate coupling regime, resulting from the resonant character of the energy transfer. This finding may offer a nontrivial quantum control knob over energy transfer at the nanoscale.
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Affiliation(s)
- Junjie Liu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Hui Xu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Baowen Li
- Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Changqin Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China
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Michelini F, Crépieux A, Beltako K. Entropy production in photovoltaic-thermoelectric nanodevices from the non-equilibrium Green's function formalism. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:175301. [PMID: 28333684 DOI: 10.1088/1361-648x/aa62e4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We discuss some thermodynamic aspects of energy conversion in electronic nanosystems able to convert light energy into electrical or/and thermal energy using the non-equilibrium Green's function formalism. In a first part, we derive the photon energy and particle currents inside a nanosystem interacting with light and in contact with two electron reservoirs at different temperatures. Energy conservation is verified, and radiation laws are discussed from electron non-equilibrium Green's functions. We further use the photon currents to formulate the rate of entropy production for steady-state nanosystems, and we recast this rate in terms of efficiency for specific photovoltaic-thermoelectric nanodevices. In a second part, a quantum dot based nanojunction is closely examined using a two-level model. We show analytically that the rate of entropy production is always positive, but we find numerically that it can reach negative values when the derived particule and energy currents are empirically modified as it is usually done for modeling realistic photovoltaic systems.
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Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems. ENTROPY 2017. [DOI: 10.3390/e19040158] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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Affiliation(s)
- Charles A. Stafford
- Department of Physics, University of Arizona, 1118 East Fourth Street, Tucson, Arizona 85721, USA
| | - Abhay Shastry
- Department of Physics, University of Arizona, 1118 East Fourth Street, Tucson, Arizona 85721, USA
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Zelovich T, Hansen T, Liu ZF, Neaton JB, Kronik L, Hod O. Parameter-free driven Liouville-von Neumann approach for time-dependent electronic transport simulations in open quantum systems. J Chem Phys 2017. [DOI: 10.1063/1.4976731] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Affiliation(s)
- Tamar Zelovich
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Thorsten Hansen
- Department of Chemistry, Copenhagen University, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
| | - Zhen-Fei Liu
- Department of Physics, University of California, Berkeley, Berkeley, California 94720-7300, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Jeffrey B. Neaton
- Department of Physics, University of California, Berkeley, Berkeley, California 94720-7300, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, Berkeley, California 94720, USA
| | - Leeor Kronik
- Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel
| | - Oded Hod
- Department of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
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Newman D, Mintert F, Nazir A. Performance of a quantum heat engine at strong reservoir coupling. Phys Rev E 2017; 95:032139. [PMID: 28415330 DOI: 10.1103/physreve.95.032139] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Indexed: 06/07/2023]
Abstract
We study a quantum heat engine at strong coupling between the system and the thermal reservoirs. Exploiting a collective coordinate mapping, we incorporate system-reservoir correlations into a consistent thermodynamic analysis, thus circumventing the usual restriction to weak coupling and vanishing correlations. We apply our formalism to the example of a quantum Otto cycle, demonstrating that the performance of the engine is diminished in the strong coupling regime with respect to its weakly coupled counterpart, producing a reduced net work output and operating at a lower energy conversion efficiency. We identify costs imposed by sudden decoupling of the system and reservoirs around the cycle as being primarily responsible for the diminished performance, and we define an alternative operational procedure which can partially recover the work output and efficiency. More generally, the collective coordinate mapping holds considerable promise for wider studies of thermodynamic systems beyond weak reservoir coupling.
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Affiliation(s)
- David Newman
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Florian Mintert
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Ahsan Nazir
- Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
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Kato A, Tanimura Y. Quantum heat current under non-perturbative and non-Markovian conditions: Applications to heat machines. J Chem Phys 2016; 145:224105. [DOI: 10.1063/1.4971370] [Citation(s) in RCA: 67] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Akihito Kato
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Carrega M, Solinas P, Sassetti M, Weiss U. Energy Exchange in Driven Open Quantum Systems at Strong Coupling. PHYSICAL REVIEW LETTERS 2016; 116:240403. [PMID: 27367367 DOI: 10.1103/physrevlett.116.240403] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Indexed: 06/06/2023]
Abstract
The time-dependent energy transfer in a driven quantum system strongly coupled to a heat bath is studied within an influence functional approach. Exact formal expressions for the statistics of energy dissipation into the different channels are derived. The general method is applied to the driven dissipative two-state system. It is shown that the energy flows obey a balance relation, and that, for strong coupling, the interaction may constitute the major dissipative channel. Results in analytic form are presented for the particular value K=1/2 of strong Ohmic dissipation. The energy flows show interesting behaviors including driving-induced coherences and quantum stochastic resonances. It is found that the general characteristics persists for K near 1/2.
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Affiliation(s)
| | | | - Maura Sassetti
- SPIN-CNR, Via Dodecaneso 33, 16146 Genova, Italy
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
| | - Ulrich Weiss
- II. Institut für Theoretische Physik, Universität Stuttgart, D-70550 Stuttgart, Germany
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46
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Quantum Thermodynamics in Strong Coupling: Heat Transport and Refrigeration. ENTROPY 2016. [DOI: 10.3390/e18050186] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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47
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Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers. ENTROPY 2016. [DOI: 10.3390/e18040124] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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48
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Seifert U. First and Second Law of Thermodynamics at Strong Coupling. PHYSICAL REVIEW LETTERS 2016; 116:020601. [PMID: 26824534 DOI: 10.1103/physrevlett.116.020601] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2015] [Indexed: 06/05/2023]
Abstract
For a small driven system coupled strongly to a heat bath, internal energy and exchanged heat are identified such that they obey the usual additive form of the first law. By identifying this exchanged heat with the entropy change of the bath, the total entropy production is shown to obey an integral fluctuation theorem on the trajectory level implying the second law in the form of a Clausius inequalilty on the ensemble level. In this Hamiltonian approach, the assumption of an initially uncorrelated state is not required. The conditions under which the proposed identification of heat is unique and experimentally accessible are clarified.
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Affiliation(s)
- Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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