The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
We consider a three-stroke engine in the microscopic regime where the working body of the engine is composed of a two-level system. The working body of the engine aims to withdraw heat from the hot heat bath, generate work, and discharge the surplus heat into the cold heat bath through the successive execution of three strokes. In this process, the interaction of the working body with the heat baths is assumed to be energy-conserving and thus can be described by thermal operations. While earlier studies analyzed the optimal performance of this engine when the working body could be transformed by any arbitrary thermal operation, we present closed expressions for the maximum work produced by the engine and the maximum efficiency of the engine when only a restricted class of thermal operations can be implemented on the working body. Furthermore, we explore the engine's optimal performance under two well-studied classes of restrictions: thermal operations realized via Jaynes-Cummings interaction and thermal operations realizable with finite-sized heat baths. Therefore, on one hand, our results are general, as they reproduce the optimal performance achieved when any arbitrary thermal operation can be implemented on the working body once the restriction is relaxed. On the other hand, our results allow us to determine the engine's maximum work production and efficiency in a more realistic scenario, where only a restricted class of thermal operations are possible, thereby bringing our findings closer to experimental feasibility.
We investigate the finite-power performance of quantum heat engines working in the linear response regime where the temperature gradient is small. The engine cycles with working substances of ideal harmonic systems consist of two heat transfer and two adiabatic processes, such as the Carnot cycle, Otto cycle, and Brayton cycle. By analyzing the optimal protocol under maximum power we derive the explicitly analytic expression for the irreversible entropy production, which becomes the low dissipation form in the long duration limit. Assuming the engine to be endoreversible, we derive the universal expression for the efficiency at maximum power, which agrees well with that obtained from the phenomenological heat transfer laws holding in the classical thermodynamics. Through appropriate identification of the thermodynamic fluxes and forces that a linear relation connects, we find that the quantum engines under consideration are tightly coupled, and the universality of efficiency at maximum power is confirmed at the linear order in the temperature gradient.
We study the work fluctuations in ergotropic heat engines, namely two-stroke quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exhaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non-trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3=U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs), which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.
The formulation of models describing quantum versions of heat engines plays an important role in the quest toward establishing the laws of thermodynamics in the quantum regime. Of particular importance is the description of stroke-based engines, which can operate at finite time. In this paper we put forth a framework for describing stroboscopic, two-stroke engines, in generic quantum chains. The framework is a generalization of the so-called SWAP engine and is based on a collisional model, which alternates between pure heat and pure work strokes. The transient evolution towards a limit cycle is also fully accounted for. Moreover, we show that once the limit cycle has been reached, the energy of the internal sites of the chain no longer changes, with the heat currents being associated exclusively to the boundary sites. Using a combination of analytical and numerical methods, we show that this type of engine offers multiple ways of optimizing the output power, without affecting the efficiency. Finally, we also show that there exists an entire class of models, characterized by a specific type of interchain interaction, which always operate at Otto efficiency, irrespective of the operating conditions of the reservoirs.
This paper explores quantum heat engines based on qubit and qutrit working media interacting with thermal environments through generalized amplitude damping (GAD) channels. We investigate how quantum channels can be employed to model heat absorption, dissipation, and work extraction in open quantum thermal machines, and derive the conditions required for positive work extraction. The effects of quantum correlations, emission probability, population redistribution, and system--environment interactions on the thermodynamic performance of the engine are systematically analyzed across different operational regimes. In addition, we examine the ergotropy of qubit and qutrit systems under dissipative dynamics to understand how environmental effects influence the maximum extractable work. Our results demonstrate that multilevel quantum systems exhibit enhanced work extraction capability and improved robustness against decoherence compared to two-level systems, providing further insight into the role of dissipative dynamics and quantum resources in realistic quantum thermodynamic devices.
Quantum heat engines are devices comprised of one or more quantum systems operating cyclically between two heat reservoirs to produce work.Although the laws of quantum mechanics rule these engines, this does not imply that these machines function in a quantum fashion, or exhibit a quantum advantage.Indeed, quantum heat engines have shown a remarkable similarity with classical models, thus raising the question of what is "quantum" in quantum thermodynamics.With the help of the P-representability concept, an expression called classicality function is introduced -allowing us to quantify the degree of non-classicality of a bosonic system.As an illustration, we consider a quantum heat engine consisting of a single bosonic mode as a working substance coupled to a cold thermal and hot squeezed thermal bath.For two specific protocols, i.e., a quantum Otto and a generalized cycle, we show that the non-classicality is a resource that can be used to perform thermodynamical tasks more efficiently.Furthermore, we present a theoretical framework to study how quantum features, such as entanglement or coherence, affect the classical formulations of thermodynamic axioms.