Search Results (15)

We present a comprehensive theoretical investigation about the operational regions of quantum systems, specifically examining their roles as working media functioning between two thermal reservoirs in quantum thermal machines (QTMs). This study provides relevant and novel insights, including a complete spectrum of QTMs within the operational region of these quantum systems, and introduces new QTM designs never before described in the literature. Additionally, this work introduces a standardized and cohesive classification scheme for QTMs, ensuring robustness in nomenclature and operational distinctions, which enhances both theoretical understanding and practical application. Notably, one of these designs directly addresses the need for a more appropriate explanation of the operation of a laser (or maser) as a QTM. Initial calculations were performed to achieve results applicable to any quantum system subjected to rules analogous to those used in classical thermal machine studies. These results were then used to analyze two-level quantum systems as the working medium of QTMs in the Otto cycle. In particular, we analyzed two specific quantum systems: the laser and a spinless electron in a one-dimensional quantum ring, yielding consistent and innovative results. Overall, this study offers valuable insights into the operation and classification of QTMs, establishing a clear and unified framework for their nomenclature while opening new avenues for the design and enhancement of these devices. Full article

Quantum heat engines (QHEs) are established by applying the principles of quantum thermodynamics to small−scale systems, which leverage quantum effects to gain certain advantages. In this study, we investigate the quantum Otto cycle by employing the dipole−dipole coupled polar molecules as the working substance of QHE. Here, the molecules are considered to be trapped within an optical lattice and located in an external electric field. We analyze the work output and the efficiency of the quantum Otto heat engine (QOHE) as a function of various physical parameters, including electric field strength, dipole−dipole interaction and temperatures of heat baths. It is found that by adjusting these physical parameters the performance of the QOHE can be optimized effectively. Moreover, we also examine the influences of the entanglement and relative entropy of coherence for the polar molecules in thermal equilibrium states on the QOHE. Our results demonstrate the potential of polar molecules in achieving QHEs. Full article

In this work, we lay the foundations for computing the behavior of a quantum heat engine whose working medium consists of an ensemble of non-harmonic quantum oscillators. In order to enable this analysis, we develop a method based on the Schrödinger picture. We investigate different possible choices on the basis of expanding the density operator, as it is crucial to select a basis that will expedite the numerical integration of the time-evolution equation without compromising the accuracy of the computed results. For this purpose, we developed an estimation technique that allows us to quantify the error that is unavoidably introduced when time-evolving the density matrix expansion over a finite-dimensional basis. Using this and other ways of evaluating a specific choice of basis, we arrive at the conclusion that the basis of eigenstates of a harmonic Hamiltonian leads to the best computational performance. Additionally, we present a method to quantify and reduce the error that is introduced when extracting relevant physical information about the ensemble of oscillators. The techniques presented here are specific to quantum heat cycles; the coexistence within a cycle of time-dependent Hamiltonian and coupling with a thermal reservoir are particularly complex to handle for the non-harmonic case. The present investigation is paving the way for numerical analysis of non-harmonic quantum heat machines. Full article

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 $U_1$, an idle swap $U_2$ (where one of the qutrits is regarded as an effective qubit), and a non-trivial permutation of energy eigenstates $U_3$, which indeed corresponds to the composition of the two previous unitaries, namely $U_3=U_2{U}_1$. While $U_1$ and $U_2$ are Hermitian (and hence involutions), $U_3$ 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 $U_3$. Full article

We examine the performance of a finite-time, endoreversible Otto heat engine with a working medium of monolayer or multilayered graphene subjected to an external magnetic field. As the energy spectrum of multilayer graphene under an external magnetic field depends strongly on the number of layers, so too does its thermodynamic behavior. We show that this leads to a simple relationship between the engine efficiency and the number of layers of graphene in the working medium. Furthermore, we find that the efficiency at maximum power for bilayer and trilayer working mediums can exceed that of a classical endoreversible Otto cycle. Conversely, a working medium of monolayer graphene displays identical efficiency at maximum power to a classical working medium. These results demonstrate that layered graphene can be a useful material for the construction of efficient thermal machines for diverse quantum device applications. Full article

We study the performance of an endoreversible magnetic Otto cycle with a working substance composed of a single quantum dot described using the well-known Fock–Darwin model. We find that tuning the intensity of the parabolic trap (geometrical confinement) impacts the proposed cycle’s performance, quantified by the power, work, efficiency, and parameter region where the cycle operates as an engine. We demonstrate that a parameter region exists where the efficiency at maximum output power exceeds the Curzon–Ahlborn efficiency, the efficiency at maximum power achieved by a classical working substance. Full article

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance. Full article

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production. Full article

In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced. Full article

In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine. Full article

We studied the performance of classical and quantum magnetic Otto cycle with a working substance composed of a single quantum dot using the Fock–Darwin model with the inclusion of the Zeeman interaction. Modulating an external/perpendicular magnetic field, in the classical approach, we found an oscillating behavior in the total work extracted that was not present in the quantum formulation.We found that, in the classical approach, the engine yielded a greater performance in terms of total work extracted and efficiency than when compared with the quantum approach. This is because, in the classical case, the working substance can be in thermal equilibrium at each point of the cycle, which maximizes the energy extracted in the adiabatic strokes. Full article

Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources. An instrumental question is how their performance measures up against the efficiency of classical engines. For single ion engines undergoing quantum Otto cycles it has been found that the efficiency at maximal power is given by the Curzon–Ahlborn efficiency. This is rather remarkable as the Curzon–Alhbron efficiency was originally derived for endoreversible Carnot cycles. Here, we analyze two examples of endoreversible Otto engines within the same conceptual framework as Curzon and Ahlborn’s original treatment. We find that for endoreversible Otto cycles in classical harmonic oscillators the efficiency at maximal power is, indeed, given by the Curzon–Ahlborn efficiency. However, we also find that the efficiency of Otto engines made of quantum harmonic oscillators is significantly larger. Full article

The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero. Full article

The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases. Full article

On the basis of introducing the origin and development of finite time thermodynamics (FTT), this paper reviews the progress in FTT optimization for internal combustion engine (ICE) cycles from the following four aspects: the studies on the optimum performances of air standard endoreversible (with only the irreversibility of heat resistance) and irreversible ICE cycles, including Otto, Diesel, Atkinson, Brayton, Dual, Miller, Porous Medium and Universal cycles with constant specific heats, variable specific heats, and variable specific ratio of the conventional and quantum working fluids (WFs); the studies on the optimum piston motion (OPM) trajectories of ICE cycles, including Otto and Diesel cycles with Newtonian and other heat transfer laws; the studies on the performance limits of ICE cycles with non-uniform WF with Newtonian and other heat transfer laws; as well as the studies on the performance simulation of ICE cycles. In the studies, the optimization objectives include work, power, power density, efficiency, entropy generation rate, ecological function, and so on. The further direction for the studies is explored. Full article