Impurity reveals distinct operational phases in quantum thermodynamic cycles

2022-11-04

Aditya Prakash , Abhishek Kumar , Colin Benjamin

We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square … We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well (ISW) potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong and weak coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are non-trivially affected by the impurity.

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Non-Markovian effect on quantum Otto engine: Going beyond the Carnot efficiency

2020-06-24

Yuji Shirai , Kazunari Hashimoto , Ryuta Tezuka +2 more

Enhancement of thermal efficiency of quantum heat engines has been discussed mainly in terms of quantumness of working substances. In the present study, we propose as another possibility to utilize … Enhancement of thermal efficiency of quantum heat engines has been discussed mainly in terms of quantumness of working substances. In the present study, we propose as another possibility to utilize a quantum-mechanical (reversible) feature of system-reservoir interaction, which reveals itself in the short-time regime as a non-Markovian effect on the reduced dynamics of the substance, before asymptotically approaching irreversible processes. For this purpose, we study a limit cycle of the quantum Otto engine comprising a working two-level system and two reservoirs, including the non-Markovian effect for the finite-time isochoric processes while the work-extracting processes are kept quantum adiabatic. Assuming that the system interacts weakly with the reservoirs consisting of infinite bosons, we find a parameter regime beyond the Carnot efficiency in which a positive work is extracted by including a non-Markovian effect called energy backflow. We also find that the interaction energy is finite and contributes to the positive work even for the weak interaction. The work diminishes if we include into the work the energy for detaching the working substance from reservoirs.

Role of quantum correlations in light-matter quantum heat engines

2017-11-16

G. Alvarado Barrios , F. Albarrán-Arriagada , F. A. Cárdenas-López +2 more

We study a quantum Otto engine embedding a working substance composed by a two-level system interacting with a harmonic mode. The physical properties of the substance are described by a … We study a quantum Otto engine embedding a working substance composed by a two-level system interacting with a harmonic mode. The physical properties of the substance are described by a generalized quantum Rabi model arising in superconducting circuits realizations. We show that light-matter quantum correlations reduction during the hot bath stage and compression stage act as a resource for enhanced work extraction and efficiency respectively. Also, we demonstrate that the anharmonic spectrum of the working subtance has a direct impact on the transition from heat engine into refrigerator as the light-matter coupling is increased. These results shed light on the search for optimal conditions in the performance of quantum heat engines.

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Light-matter quantum Otto engine in finite time

2021-01-01

G. Alvarado Barrios , F. Albarrán-Arriagada , Francisco J. Peña +2 more

We study a quantum Otto engine at finite time, where the working substance is composed of a two-level system interacting with a harmonic oscillator, described by the quantum Rabi model. … We study a quantum Otto engine at finite time, where the working substance is composed of a two-level system interacting with a harmonic oscillator, described by the quantum Rabi model. We obtain the limit cycle and calculate the total work extracted, efficiency, and power of the engine by numerically solving the master equation describing the open system dynamics. We relate the total work extracted and the efficiency at maximum power with the quantum correlations embedded in the working substance, which we consider through entanglement of formation and quantum discord. Interestingly, we find that the engine can overcome the Curzon-Ahlborn efficiency when the working substance is in the ultrastrong coupling regime. This high-efficiency regime roughly coincides with the cases where the entanglement in the working substance experiences the greatest reduction in the hot isochoric stage. Our results highlight the efficiency performance of correlated working substances for quantum heat engines.

Quantum Otto cycle under strong coupling

2022-01-01

Mao Kaneyasu , Yoshihiko Hasegawa

Quantum heat engines are often discussed under the weak coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this … Quantum heat engines are often discussed under the weak coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak coupling assumption is proposed. We replace the thermalization process in the weak coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and it indicates that when the contribution of the interaction terms is neglected in the weak interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak coupling counterpart.

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Quantum Otto cycle under strong coupling

2023-04-27

Mao Kaneyasu , Yoshihiko Hasegawa

Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption … Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.

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Performance of quantum heat engines under the influence of long-range interactions

2020-07-16

Qian Wang

We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the … We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two type of thermodynamic cycles, namely Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of long-range interacting heat engine can be boosted by long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle, there exist an optimal condition for which the largest enhancement of work output and efficiency can be achieved simultaneously by the long-range interactions. But, for the Stirling cycle, the condition that gives the largest enhancement in work output does not lead to the largest enhancement in efficiency. We also investigate how the parameter regimes under which the engine performance is enhanced by the long-range interactions is evolved with decrease in the range of interaction.

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Quantum Carnot thermal machines revisited: Definition of efficiency and the effects of strong coupling

2023-01-01

Junjie Liu , Kenneth A. Jung

Whether the strong coupling to thermal baths can improve the performance of quantum thermal machines remains an open issue under active debate. Here, we revisit quantum thermal machines operating with … Whether the strong coupling to thermal baths can improve the performance of quantum thermal machines remains an open issue under active debate. Here, we revisit quantum thermal machines operating with the quasi-static Carnot cycle and aim to unveil the role of strong coupling in maximum efficiency. Our analysis builds upon definitions of excess work and heat derived from an exact formulation of the first law of thermodynamics for the working substance, which captures the non-Gibbsian thermal equilibrium state that emerges at strong couplings during quasi-static isothermal processes. These excess definitions differ from conventional ones by an energetic cost for maintaining the non-Gibbsian characteristics. With this distinction, we point out that one can introduce two different yet thermodynamically allowed definitions for efficiency of both the heat engine and refrigerator modes. We dub them excess and hybrid definitions which differ in the way of defining the gain for the thermal machines at strong couplings by either just analyzing the energetics of the working substance or instead evaluating the performance from an external system upon which the thermal machine acts, respectively. We analytically demonstrate that the excess definition predicts that the Carnot limit remains the upper bound for both operation modes at strong couplings, whereas the hybrid one reveals that strong coupling can suppress the maximum efficiency rendering the Carnot limit unattainable. These seemingly incompatible predictions thus indicate that it is imperative to first gauge the definition for efficiency before elucidating the exact role of strong coupling, thereby shedding light on the on-going investigation on strong-coupling quantum thermal machines.

Critical-point behavior of a measurement-based quantum heat engine

2018-11-29

Suman Chand , Asoka Biswas

We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic … We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic field, we show that the system performs in a quantum Otto cycle above a critical value of the magnetic field, while below such critical point, it does not operate in a heat cycle at all. Moreover, at the critical point, its interaction with an ancillary ion deteriorates the performance of the system as a heat engine. We further show that a strong interaction between the constituent ions of an ion-based system is crucial for it to work in a heat-work cycle, while the coupling to the ancillary system must be minimized.

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Switching the function of the quantum Otto cycle in non-Markovian dynamics: Heat engine, heater, and heat pump

2023-04-27

Miku Ishizaki , Naomichi Hatano , Hiroyasu Tajima

Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted … Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.

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Switching the function of the quantum Otto cycle in non-Markovian dynamics: heat engine, heater and heat pump

2022-01-01

Miku Ishizaki , Naomichi Hatano , Hiroyasu Tajima

Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted … Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.

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The Quantum Otto Heat Engine with a relativistically moving thermal bath

2021-04-14

Nikolaos Papadatos

We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity … We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a moving heat bath and a static cold bath. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum system we obtain the total produced work, the efficiency and the efficiency at maximum power. The maximum efficiency of the Otto quantum heat engine depends only on the ratio of the minimum and maximum energy gaps. On the contrary, the efficiency at maximum power and the extracted work decreases with the velocity since the motion of the heat bath has an energy cost for the quantum heat engine. Furthermore, the efficiency at maximum power depends on the nature of the working medium.

Universal quantum Otto heat machine based on the Dicke model

2024-01-18

He-Guang Xu , Jiasen Jin , G. D. de Moraes Neto +1 more

In this paper we study a quantum Otto thermal machine where the working substance is composed of $N$ identical qubits coupled to a single mode of a bosonic field, where … In this paper we study a quantum Otto thermal machine where the working substance is composed of $N$ identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number $N$ of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.

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Quantum thermal cycles based on non-resonant exchange interactions

2020-10-07

Nicolò Piccione , Gabriele De Chiara , Bruno Bellomo

We present a detailed study of quantum thermal machines employing quantum systems as working substances. In particular, we study two different types of two-stroke cycles where two collections of identical … We present a detailed study of quantum thermal machines employing quantum systems as working substances. In particular, we study two different types of two-stroke cycles where two collections of identical quantum systems with evenly spaced energy levels are initially prepared at thermal equilibrium by putting them in contact with a cold and a hot thermal bath, respectively. The two cycles differ in the absence or the presence of a mediator system, while, in both cases, non-resonant exchange Hamiltonians are exploited as particle interactions. We show that the efficiencies of these machines depend only on the energy gaps of the systems composing the collections and are equal to the efficiency of equivalent Otto cycles. Focusing on the cases of qubits or harmonic oscillators for both models, we maximize the engine power and analyze, in the model without the mediator, the role of the waiting time between subsequent interactions. It turns out that the case with the mediator can bring performance advantages when the interaction times are comparable with the waiting time of the correspondent cycle without the mediator. We find that in both cycles, the power peaks of qubit systems can surpass the Curzon-Ahlborn efficiency. Finally, we compare our cycle without the mediator with previous schemes of the quantum Otto cycle showing that high coupling is not required to achieve the same maximum power.

The Critical Behavior of Quantum Stirling Heat Engine

2023-01-01

Yuan-Sheng Wang , Man‐Hong Yung , Dazhi Xu +2 more

We investigate the performance of a Stirling cycle with a working substance (WS) modeled as the quantum Rabi model (QRM), exploring the impact of criticality on its efficiency. Our findings … We investigate the performance of a Stirling cycle with a working substance (WS) modeled as the quantum Rabi model (QRM), exploring the impact of criticality on its efficiency. Our findings indicate that the criticality of the QRM has a positive effect on improving the efficiency of the Stirling cycle. Furthermore, we observe that the Carnot efficiency is asymptotically achievable as the WS parameter approaches the critical point, even when both the temperatures of the cold and hot reservoirs are finite. Additionally, we derive the critical behavior for the efficiency of the Stirling cycle, demonstrating how the efficiency asymptotically approaches the Carnot efficiency as the WS parameter approaches the critical point. Our work deepens the understanding of the impact of criticality on the performance of a Stirling heat engine.

Implications of Coupling in Quantum Thermodynamic Machines

2017-09-08

George Thomas , Manik Banik , Sibasish Ghosh

We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We … We study coupled quantum systems as the working media of thermodynamic machines. Under a suitable phase-space transformation, the coupled systems can be expressed as a composition of independent subsystems. We find that for the coupled systems, the figures of merit, that is the efficiency for engine and the coefficient of performance for refrigerator, are bounded (both from above and from below) by the corresponding figures of merit of the independent subsystems. We also show that the optimum work extractable from a coupled system is upper bounded by the optimum work obtained from the uncoupled system, thereby showing that the quantum correlations do not help in optimal work extraction. Further, we study two explicit examples, coupled spin-$1/2$ systems and coupled quantum oscillators with analogous interactions. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-$1/2$ systems when they work as heat engines. However, for the same interaction, the coefficient of performance behaves in a reverse manner, while the systems work as the refrigerator. Thus the same coupling can cause opposite effects in the figures of merit of heat engine and refrigerator.

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Critical behavior of the quantum Stirling heat engine

2024-02-08

Yuan-Sheng Wang , Man‐Hong Yung , Dazhi Xu +2 more

We investigate the performance of a Stirling cycle with a working substance (WS) modeled as the quantum Rabi model (QRM), exploring the impact of criticality on its efficiency. Our findings … We investigate the performance of a Stirling cycle with a working substance (WS) modeled as the quantum Rabi model (QRM), exploring the impact of criticality on its efficiency. Our findings indicate that the criticality of the QRM has a positive effect on improving the efficiency of the Stirling cycle when the WS parameters are in the normal phase. Furthermore, we observe that the Carnot efficiency is asymptotically achievable as the WS parameter approaches the critical point, even when both temperatures of the cold and hot reservoirs are finite. Additionally, we derive the critical behavior for the efficiency of the Stirling cycle, demonstrating how the efficiency asymptotically approaches the Carnot efficiency as the WS parameter approaches the critical point. Our work deepens the understanding of the impact of criticality on the performance of a Stirling heat engine.

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Performance of Coupled Systems as Quantum Thermodynamic Machines

2016-07-04

George Thomas , Manik Banik , Sibasish Ghosh

In this work, we study coupled quantum systems as working media of thermodynamic machines. With suitable co-ordinate transformation, the coupled system appears to be uncoupled in the new frame of … In this work, we study coupled quantum systems as working media of thermodynamic machines. With suitable co-ordinate transformation, the coupled system appears to be uncoupled in the new frame of reference. In that case, the global efficiency of the total system is bounded (both from above and below) by the efficiencies of the independent subsystems, provided both the independent subsystems work in the engine mode. This is also true for the coefficient of performance when the coupled system behave as refrigerator. We make a comparative study between coupled spin-$1/2$ systems and coupled quantum oscillators considering analogous interaction for both the systems. Interestingly, for particular kind of interactions, the efficiency of the coupled oscillators outperforms that of the coupled spin-$1/2$ systems when they work as heat engines. However, for same interaction, the coefficient of performance behaves in a reverse manner, while the system work as refrigerator. Therefore coupling can cause opposite effects in the figure of merits of heat engine and refrigerator.

Powering quantum Otto engines only with q-deformation of the working substance

2023-01-01

Fatih Özaydin , Özgür E. Müstecaplıoğlu , T. Hakioḡlu

We consider a quantum Otto cycle with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the … We consider a quantum Otto cycle with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the cycle. In usual quantum Otto cycle, a Hamiltonian parameter is varied during the quantum adiabatic stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a quantum Otto cycle without any classical analog.

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Quantum Engines and Refrigerators

2023-01-01

L. M. Cangemi , Chitrak Bhadra , Amikam Levy

Engines are systems and devices that convert one form of energy into another, typically into a more useful form that can perform work. In the classical setup, physical, chemical, and … Engines are systems and devices that convert one form of energy into another, typically into a more useful form that can perform work. In the classical setup, physical, chemical, and biological engines largely involve the conversion of heat into work. This energy conversion is at the core of thermodynamic laws and principles and is codified in textbook material. In the quantum regime, however, the principles of energy conversion become ambiguous, since quantum phenomena come into play. As with classical thermodynamics, fundamental principles can be explored through engines and refrigerators, but, in the quantum case, these devices are miniaturized and their operations involve uniquely quantum effects. Our work provides a broad overview of this active field of quantum engines and refrigerators, reviewing the latest theoretical proposals and experimental realizations. We cover myriad aspects of these devices, starting with the basic concepts of quantum analogs to the classical thermodynamic cycle and continuing with different quantum features of energy conversion that span many branches of quantum mechanics. These features include quantum fluctuations that become dominant in the microscale, non-thermal resources that fuel the engines, and the possibility of scaling up the working medium's size, to account for collective phenomena in many-body heat engines. Furthermore, we review studies of quantum engines operating in the strong system-bath coupling regime and those that include non-Markovian phenomena. Recent advances in thermoelectric devices and quantum information perspectives, including quantum measurement and feedback in quantum engines, are also presented.

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Impurity reveals distinct operational phases in quantum thermodynamic cycles

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