Robert Alicki
There exists a consistent thermodynamical formalism with canonical definition of local temperatures which allows to extend the Carnot bound also to non-equilibrium baths, like those discussed in the Letter
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A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical proce…
In order to build a quantum analog of traditional Carnot engine, a common choice is replacing the two thermodynamic adiabatic processes with two quantum mechanical adiabatic processes. In general, such quantum Carnot engine has six strokes. We analyze the efficiency of such six-stroke quantum Carnot engine in a perturbative way.
We study the physical implementation of the Photon Carnot engine (PCE) based on the cavity QED system [M. Scully et al, Science, \textbf{299}, 862 (2003)]. Here, we analyze two decoherence mechanisms for the more practical systems of PCE, the dissipation of photon field and the pure dephasing of the input atoms. As a result we find that (I) the PCE can work well to some extent even in the existence of the cavity loss (photon dissipation); and (II) the short-time atomic dephasing, which can destroy the PCE, is a fatal problem to be overcome.
Heat engines extract work by running cyclically between two heat reservoirs. When the two reservoirs are thermal and at different temperatures, the maximum efficiency of the engine is given by the Carnot limit. Here we consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to an engineered squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, exponentially approaching unity for large squeezing parameters $r$. Furthermore, we propose an experimental scheme to implement such a system by using a single trapped ion …
A heat engine operating in the one-shot finite-size regime, where systems composed of a small number of quantum particles interact with hot and cold baths and are restricted to one-shot measurements, delivers fluctuating work. Further, engines with lesser fluctuation produce a lesser amount of deterministic work. Hence, the heat-to-work conversion efficiency stays well below the Carnot efficiency. Here we overcome this limitation and attain Carnot efficiency in the one-shot finite-size regime, where the engines allow the working systems to simultaneously interact with two baths via the semi-lo…
The Performance Analysis of a Quantum-Mechanical Carnot-like Engine using Diatomic Molecules
提出以 Morse 振子为工质的量子力学类卡诺循环模型，在有限速移动势阱下分析效率、功率及最优工作区间，结果与其他工质发动机一致。
We investigate scaling of work and efficiency of a photonic Carnot engine with the number of quantum coherent resources. Specifically, we consider a generalization of the "phaseonium fuel" for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by [M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther, Science {\bf 299}, 862 (2003)], to the case of $N+1$ level atoms with $N$ coherent lower levels. We take into account atomic relaxation and dephasing as well as the cavity loss and derive a coarse grained…
It is possible to extract work from a quantum-mechanical system whose dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is required to operate such a quantum engine in place of the heat bath used to run a conventional classical thermodynamic heat engine. The effect of the energy bath is to maintain the expectation value of the system Hamiltonian during an isoenergetic expansion. It is shown that the existence of such a bath leads to equilibrium quantum states that maximise the von Neumann entropy. Quantum analogues of certain thermodynamic relations are obtained that …
A quantum-mechanical analog of the Carnot engine reversibly working at vanishing temperature, shortly termed the quantum-mechanical Carnot engine, is discussed. A general formula for the efficiency of such an engine with an arbitrary confining potential is presented. Its expression is purely given in terms of the structure of the energy spectrum. Dependency of the efficiency on the form of a potential as an analog of the working material in thermodynamics implies nonuniversality of the engine. This may be due to the absence of the second-law-like principle in pure-state quantum mechanics.
Unbounded Work Extraction and Zero Work Fluctuations in a Super-Carnot Otto Information Engine
该研究在量子奥托循环中引入两个连续麦克斯韦妖，构建奥托信息引擎，实现仅依赖能级间隙的无界功提取和零功涨落，且效率可超越卡诺极限，并具有优越输出功率。
A role of the superposition principle is discussed for the quantum-mechanical Carnot engine introduced by Bender, Brody, and Meister [J. Phys. A 33, 4427 (2000)]. It is shown that the efficiency of the engine can be enhanced by superposition of quantum states. A finite-time process is also discussed, and the condition of the maximum power output is presented. Interestingly, the efficiency at the maximum power is lower than that without superposition.
Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics. In particular, we will show that rather the definition of heat has to be modified to account for the thermodynamic cost for maintaining coherence and entanglement. Our theoretical findings are numerically illus…
Entropy-based analysis of single-qubit Otto and Carnot heat engines
该研究基于熵基理论分析了单量子比特Otto和Carnot热机的效率，揭示了相干工作与熵生成对热机性能的影响。
Beyond the Carnot Limit in the Internal Cycles of a Quantum Heat Engine under Finite Heat Reservoirs
本文解析研究了耦合有限热库的微观量子热机卡诺循环，证明其内部循环可在不消耗额外量子资源的情况下超越标准卡诺极限，并揭示了有限热库热容量对最大效率和功率输出的关键作用。
The Anyonic Quantum Carnot Engine
本文研究以二维任意子为介质的量子卡诺热机，推导出其效率的显式表达式，为探索小尺度量子系统的热力学及从量子统计中提取机械功提供了新途径。
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical mechanical entropy is defined by Gibbs. The relation between these two definitions of entropy is still not fully explored. In this work, we study this problem by employing the phase-space formulation of quantum mechanics. For those quantum states having well-defined classical counterparts, we study the quantum-classical correspondence and quantum cor…
Efficiency at maximum power of a Carnot quantum information engine
本文针对量子信息引擎，提出了广义有限时间Carnot循环，在低耗散区间优化功率输出，推导出适用于任意工作介质的最大功率效率通用公式，并研究了弱能量测量下qubit信息引擎的最优性能。
In this work an example of a cyclic engine based on a quantum-mechanical properties of the strongly non linear quantum oscillator described by the Poschl-Teller [PT] model is examined. Using the [PT] model as shown in our earlier works [1-4], a quantum-mechanical analog of Carnot cycle (i.e quantum heat engine) has been constructed through the changes of both, the width L of the well and its quantum state. This quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes. The efficiency of the quantum engine based on the Poschl-Teller-like potential is derived and i…
Power-efficiency-stability trade-off in quantum information engines
该研究聚焦有限时间量子Carnot信息引擎的功率-效率-稳定性权衡，通过解析计算输出功的均值与方差，证明其可在有限功输出及涨落下达最大效率，且稳定性优于常规量子Carnot热机。
We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine mod…
An Information-Theoretic Bound on Thermodynamic Efficiency and the Generalized Carnot's Theorem
本文推导了热机效率的更严格界限，适用于经典和量子热机，并展示了量子点与费米浴耦合的引擎可达到该界限，为实际能量收集设备提供设计原理。
Information-Assisted Carnot Engine Surpasses Standard Thermodynamic Bounds
本文提出卡诺信息机，定量揭示信息与热机性能的关系，证明其可超越标准卡诺效率并实现100%效率，并用自旋-1/2系统和囚禁离子方案加以验证。
Approaching Carnot Efficiency at Finite Power in an Experimentally Feasible Quantum Heat Engine
研究热机在有限功率下逼近卡诺效率的问题，提出用超导电路热机模拟集体增强来实现，此结果规避了经典马尔可夫热机功率-效率权衡，连接抽象界限与具体平台，为量子器件设计提供途径。
We want to understand whether and to which extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e. not purposefully-designed) engine-bath interactions, the work-optimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is the Levinthal's paradox in the …
The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation $ΔS^{(\mathrm{ir})}$ on the operation time $τ$, i.e., $ΔS^{(\mathrm{ir})}\propto1/τ$. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the $1/τ$-scaling. In this paper, using a two-level atomic heat engine a…
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through the changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal ind…
Based on a quantum thermodynamic protocol for shortcut to isothermality that smoothly modify the system-reservoir interaction can significantly speed up an isothermal process while keeping the overall dissipation constant [Phys. Rev. X. 10, 031015 (2020)], we extend the study of optimization performance of Carnot-like heat engines and refrigerators in a straightforward and unified way. We derive the universal optimization efficiency of heat engines and the optimization coefficient of performance of refrigerators under two unified optimization criterions, i.e., chi criterion and omega criterion…
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot m…
Carnot's theorem poses a fundamental limit on the maximum efficiency achievable from an engine that works between two reservoirs at thermal equilibrium. We extend this result to the case of arbitrary nonthermal stationary reservoirs, even with quantum coherence. In order to do this we prove that a single nonthermal reservoir is formally equivalent to multiple equilibrium ones. Finally, we discuss the possibility of realizing an engine that works at unit efficiency by exploiting quantum coherence present in the reservoir.
The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS]…
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quan…
The efficiency of cyclic heat engines is limited by the Carnot bound. This bound follows from the second law of thermodynamics and is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. By contrast, the efficiency of engines powered by quantum non-thermal baths has been claimed to surpass the thermodynamic Carnot bound. The key to understanding the performance of such engines is a proper division of the energy supplied by the bath to the system into heat and work, depending on the associated change in the sys…
We propose a spin-star network, where a central spin-$1/2$ is coupled with XXZ interaction to $N$ outer spin-$1/2$ particles, as a quantum fuel. If the network is in thermal equilibrium with a cold bath, the central spin can have an effective temperature larger than the bath one and scaling nonlinearly with $N$. The nonlinearity can be tuned to $N^2, N^3$ or $N^4$ with the anisotropy parameter of the coupling. Using a stream of central-spin particles to pump a micromaser cavity, we calculate the dynamics of the cavity field using a coarse-grained master equation. Our study reveals that the cen…
A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of "work" is cruci…
Quantum Stirling heat engine based on Two-qubit Quantum Rabi Model with Spin-Spin Coupling
该研究以含自旋-自旋耦合的双量子比特量子Rabi模型为工质量子斯特林热机，提出参数优化策略，揭示了不同相区、不同参数对热机效率的影响规律，为量子热机效率优化提供了可行方法。
Holographic Stirling engines and the route to Carnot efficiency
研究斯特林机在不同工质下的效率，探讨再生机制对效率提升的作用，揭示实现卡诺效率的条件。
Various quantum systems are considered as the working substance for the analysis of quantum heat cycles and quantum refrigerators. The ongoing technological challenge is how efficiently can a heat engine convert thermal energy to mechanical work. The seminal work of Carnot has proposed a fundamental upper limit-the Carnot limit on the efficiency of the heat engine. However, the heat engines can be operated beyond the fundamental upper limit by exploiting non-equilibrium reservoirs. Here, the change in the space structure introduces the non-equilibrium effect. So, a question arises whether a ch…
The optimization of finite-time thermodynamic heat engines was intensively explored recently, yet limited to few cycles, e.g. finite-time Carnot-like cycle. In this paper, we supplement a new type of finite-time engine with quantum Otto cycle and show the better performance. The current model can be widely utilized benefited from the general \mathcal{C}/τ^{2} scaling of extra work for finite-time adiabatic process with long control time τ. Such scaling allows analytical optimization of the generic finite-time quantum Otto cycle to surpass the efficiency at maximum power for the Carnot-like eng…
Surpassing Carnot efficiency with relativistic motion
研究相对论运动对热机性能的影响，利用Unruh-DeWitt探测器作为工作介质，通过速度调节有效温度，实现超越静止系卡诺效率的热机。
We construct the smallest possible self contained heat engines; one composed of only two qubits, the other of only a single qutrit. The engines are self-contained as they do not require external sources of work and/or control. They are able to produce work which is used to continuously lift a weight. Despite the dimension of the engine being small, it is still able to operate at the Carnot efficiency.
We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like atmosphere. The engine first gets an energy intake, which can be done in arbitrary non-equilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits th…
We consider the optimization of a finite-time Carnot engine characterized by small dissipations. We bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point, which can be thus chosen optimally. Remarkably, this optimal point is independent of the figure of merit combining power and efficiency that is being maximized. Furthermore, for a general class of dynamics the power output becomes proportional to the heat capacity of the working substance. Since the heat capacity can scale supra-extensively with the number of const…
We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functi…
We present a (random) mechanical model consisting of two lottery-like reservoirs at altitude $E_h$ and $E_l<E_h$, respectively, in the earth's gravitational field. Both reservoirs consist of $N$ possible ball locations. The upper reservoir contains initially $n_h\le N$ weight-1 balls and the lower reservoir contains initially $n_l\le N$ weight-1 balls. Empty locations are treated as weight-0 balls. These reservoirs are being shaken up so that all possible ball configurations are equally likely to occur. A cycle consists of exchanging a ball randomly picked from the higher reservoir and a ball …
Beyond the Carnot limit: work extraction via an entropy battery
本研究探索多守恒量系综的熵转移，证明其驱动的量子热机无需诱导量子相干即可在最大功率下超越卡诺效率提取功，还明确热自旋库热力学性质，为高效量子器件奠定基础。
The quantum analog of Carnot cycles in few-particle systems consists of two quantum adiabatic steps and two isothermal steps. This construction is formally justified by use of a minimum work principle. It is then shown, without relying on any microscopic interpretations of work or heat, that the heat-to-work efficiency of the quantum Carnot cycle thus constructed may be further optimized, provided that two conditions regarding the expectation value of some generalized force operators evaluated at equilibrium states are satisfied. In general the optimized efficiency is system-specific, lower th…
Efficiency at maximum $\dotΩ$ figure of merit of a spin half quantum heat engine in the presence of external magnetic field
本文研究外磁场下以自旋半粒子为工质的有限时间量子热机，发现其在最大$\dotΩ$品质因数下的效率可超过已知界限并接近卡诺效率，表明粒子布居数的集体量子效应能显著提升热机性能。
We study the stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency larger than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) is illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We disc…
Sadi Carnot's theorem regarding the maximum efficiency of heat engines is considered to be of fundamental importance in thermodynamics. This theorem famously states that the maximum efficiency depends only on the temperature of the heat baths used by the engine, but not on the specific structure of baths. Here, we show that when the heat baths are finite in size, and when the engine operates in the quantum nanoregime, a revision to this statement is required. We show that one may still achieve the Carnot efficiency, when certain conditions on the bath structure are satisfied; however if that i…
We consider a class of quantum heat engines consisting of two subsystems interacting via a unitary transformation and coupled to two separate baths at different temperatures $T_h > T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addi…
The Critical Behavior of Quantum Stirling Heat Engine
该研究以量子 Rabi 模型为工作物质分析斯特林热机，揭示临界性可提升效率，并推导效率在临界点附近渐近趋于卡诺效率的行为。
A long standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investigated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy released from the engine to the cold bath remain…
Heat engines with single-shot deterministic work extraction
该研究提出了一种在纳米尺度上工作的热机，通过单次确定性功提取和相关性创建，实现了接近卡诺效率的热机效率。
Owing to the ubiquity of synchronization in the classical world, it is interesting to study its behavior in quantum systems. Though quantum synchronisation has been investigated in many systems, a clear connection to quantum technology applications is lacking. We bridge this gap and show that nanoscale heat engines are a natural platform to study quantum synchronization and always possess a stable limit cycle. Furthermore, we demonstrate an intimate relationship between the power of a heat engine and its phase-locking properties by proving that synchronization places an upper bound on the achi…
Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriate in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the …
The quest to identify the best heat engine has been at the center of science and technology. Thermoelectric nanoscale heat engines convert heat flows into useful work in the form of electrical power and promise the realization of on-chip power production. Considerable studies have so far revealed the potentials to yield an enhanced efficiency originating from quantum confinement effects and energy-dependent transport properties. However, the full benefit of many-body interactions in thermoelectric is yet to be investigated; identifying the optimal interaction is a hard problem due to combinato…
Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as it's working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structu…
Turning a superconducting diode into a Feynman ratchet to realize a nanoscale heat engine
该研究提出基于约瑟夫森结的超导二极管型费曼棘轮，实现纳米级热机，可从温度梯度的热涨落中做功，还分析其功率、效率及反向运行作珀尔帖冷却器的条件。
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