The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is composed of an ensemble of harmonic oscillators. A link is established between the quantum observables and thermodynamical variables based on the concept of canonical invariance. These quantum variables are sufficient to determine the state of the system and with it all thermodynamical variables. Conditions for optimal work, power and entropy production show that maximum power is a compromise between the quasistatic limit of adiabatic following on the compression and expansion branches and a sudden limit of very short time allocation to these branches. At high temperatures and quasistatic operating conditions the efficiency at maximum power coincides with the endoreversible result. The optimal compression ratio varies from the square root of the temperature ratio in the quasistatic limit where their reversibility is dominated by heat conductance to the temperature ratio to the power of 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.
The aim of this paper is to determine lost works in a molecular engine and compare results with macro (classical) heat engines. Firstly, irreversible thermodynamics are reviewed for macro and molecular cycles. Secondly, irreversible thermodynamics approaches are applied for a quantum heat engine with -1/2 spin system. Finally, lost works are determined for considered system and results show that macro and molecular heat engines obey same limitations. Moreover, a quantum thermodynamic approach is suggested in order to explain the results previously obtained from an atomic viewpoint.
We investigate the influences of quantum many-body effects, such as criticality and the existence of factorisation fields, in the thermodynamic cost of establishing a bonding link between two independent quantum spin chains. We provide a physical interpretation of the behavior of irreversible work spent in such process by linking the phenomenology of such quantities to the properties of the spectrum of the system
Irreversible logic is at odds with unitary quantum evolution. Emulating such operations by classical measurements can result in disturbances and high resource demands. To overcome these limitations, we propose protocols that harness dissipation to realize the nonunitary evolution required for irreversible gate operations. Using additional excited states subject to decay, we engineer effective decay processes that perform the desired gate operations on the smallest stable Hilbert space. These operate deterministically and in an autonomous fashion, without the need for measurements. We exemplify…
In this paper, we explore the emergence of the Wigner entropy production rate in the stationary state of a two-mode Gaussian system. The interacting modes dissipate into different local thermal baths. Also, one of the bosonic modes evolves into the squeezed-thermal state because of the parametric amplification process. Using the Heisenberg-Langevin approach, combined with quantum phase space formulation, we get an analytical expression for the steady-state Wigner entropy production rate. It contains two key terms. The first one is an Onsager-like expression that describes heat flow within the …
Bose-Einstein condensates can be used to produce work by tuning the strength of the interparticle interactions with the help of Feshbach resonances. In inhomogeneous potentials, these interaction ramps change the volume of the trapped gas allowing one to create a thermodynamic cycle known as the Feshbach engine. However, in order to obtain a large power output, the engine strokes must be performed on a short timescale, which is in contrast with the fact that the efficiency of the engine is reduced by irreversible work if the strokes are done in a non-adiabatic fashion. Here we investigate how …
We show that a pair of quantized cavity modes interacting with a spectrally broadened ensemble of Lambda-type atoms is analogous to an ensemble of two level systems coupled to a bosonic reservoir. This provides the possibility for an irreversible photon transfer between photon modes. The density of states as well as the quantum state of the reservoir can be engineered allowing the observation of effects such as the quantum Zeno- and anti-Zeno effect, the destructive interference of decay channels and the decay in a squeezed vacuum. As a particular application we discuss a photon diode, i.e. a …
A quantum thermodynamic cycle with a chiral multiferroic working substance such as $\textrm{LiCu}_{2}\textrm{O}_{2}$ is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite time quantum thermodynamic cycle which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e. the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between of the spin and the electric p…
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 t…
For heat engines working between two heat baths, functionality is often conditioned on a set of fixed constraints such as given internal structure of the engine and given temperatures for the baths. It is, however, important to devise heat engines which can function adaptively, in particular when the engine is a quantum system and the baths are subject to fluctuations. Here we study a model for an adaptive quantum heat engine whose heat baths can have variable temperatures. We obtain conditions under which such an engine can still operate. Moreover, we propose an enhancement of the heat engine…
We investigate the quantum Zeno and anti-Zeno effects for the irreversible quantum tunneling from a quantum dot to a ring array of quantum dots. By modeling the total system with the Anderson-Fano-Lee model, it is found that the transition from the quantum Zeno effect to quantum anti-Zeno effect can happen as the magnetic flux and the gate voltage were adjusted.
We introduce a new quantum heat engine, in which the working medium is a quantum system with a discrete level and a continuum. Net work done by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and the low-temperature limits, but it operates differently in temperatures between them. The efficiency of this quantum heat engine is also presented and discussed.
The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered so as to realize virtually any thermodynamic cycle. In spite of their versatility such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their …
We analyze an autonomous thermoelectric engine composed of two superconducting qubits coupled to separate heat baths and connected by a Josephson junction. Work and heat are process quantities and not observables of the engine quantum system, but their rates can be derived from the steady state expectation value of appropriate system observables and their fluctuations are given by correlation functions determined with the GKLS master equation and quantum regression theorem. The correlation functions also reveal a cyclical, dynamical transfer of energy - the strokes of the engine - hiding under…
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…
We propose an arbitrary driven spin as the working fluid of a quantum Otto cycle in the presence of internal friction. The role of total allocated time to the adiabatic branches of the cycle, generated by different control field profiles, on the extractable work and the thermal efficiency are analyzed in detail. The internal friction is characterized by the excess entropy production and quantitatively determined by studying the closeness of an actual unitary process to an infinitely long one via quantum relative entropy. It is found that the non-ideal, finite-time adiabatic transformations neg…
A heat engine is a machine which uses the temperature difference between a hot and a cold reservoir to extract work. Here both reservoirs are quantum systems and a heat engine is described by a unitary transformation which decreases the average energy of the bipartite system. On the molecular scale, the ability of implementing such a unitary heat engine is closely connected to the ability of performing logical operations and classical computing. This is shown by several examples: (1) The most elementary heat engine is a SWAP-gate acting on 1 hot and 1 cold two-level systems with different ener…
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.
We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference …
A quantum model of a heat engine resembling the Otto cycle is employed to explore strategies to suppress frictional losses. These losses are caused by the inability of the engine's working medium to follow adiabatically the change in the Hamiltonian during the expansion and compression stages. By adding external noise to the engine, frictional losses can be suppressed.
By using a laser and maser in tandem, it is possible to obtain laser action in the hot exhaust gases involved in heat engine operation. Such a "quantum afterburner" involves the internal quantum states of working gas atoms or molecules as well as the techniques of cavity quantum electrodynamics and is therefore in the domain of quantum thermodynamics. As an example, it is shown that Otto cycle engine performance can be improved beyond that of the "ideal" Otto heat engine.
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.
Landauer's erasure principle is a cornerstone of thermodynamics and information theory. According to this principle, erasing information incurs a minimum energy cost. Recently, Vaccaro and Barnett [Proc. R. Soc {\bf 467}, 1770 (2011)] explored information erasure in the context of multiple conserved quantities and showed that the erasure cost can be solely in terms of spin angular momentum. As Landauer's erasure principle plays a fundamental role in heat engines, their result considerably widens the possible configurations that heat engines can have. Motivated by this, we propose here a novel …
We describe how electromagnetically induced transparency may be used to construct a non-traditional near-ideal quantum heat engine as constrained by the Second Law. The engine is pumped by a thermal reservoir that may be either hotter or colder than that of an exhaust reservoir, and also by a monochromatic laser. As output, it produces a bright narrow emission at line center of an otherwise absorbing transition.
There is intense effort into understanding the universal properties of finite-time models of thermal machines---at optimal performance---such as efficiency at maximum power, coefficient of performance at maximum cooling power, and other such criteria. In this letter, a {\it global} principle consistent with linear irreversible thermodynamics is proposed for the whole cycle---without considering details of irreversibilities in the individual steps of the cycle. This helps to express the total duration of the cycle as $τ\propto {\bar{Q}^2}/{Δ_{\rm tot} S}$, where $\bar{Q}$ models the effective h…
We have found the optimal condition of the work performed by the quantum Szilard engine (SZE) containing multi-particles. Usually the optimal work of a cyclic engine is achieved when the whole thermodynamic process is reversible. Although the quantum SZE inherently contains an irreversible process, we can still define effectively reversible protocol based upon the force of time-forward and time-backward processes.
We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be ex…
The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of \mathscr{C}/t relation of the irreversible entropy generation S^{(\mathrm{ir})}, and show the explicit dependence of the coefficient \mathscr{C} on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such dependence allo…
The energy conversion efficiency of far-from-equilibrium systems is generally limited by irreversible thermodynamic fluxes that make contact with different heat baths. For complex systems, the states of the maximum efficiency and the minimum entropy production are usually not equivalent. Here we show that the proper adjustments of the interaction between the energy and matter currents offer some important criteria for the performance characterizations of thermal agents, regardless of the system types and transition protocols. The universal thermodynamic coupling rule plays a critical role in i…
In this work, we introduce the concept of the fractional quantum heat engine. We examine the space-fractional quantum Szilard heat engine as an example to show that the space-fractional quantum heat engines can produce higher efficiency than the conventional quantum heat engines.
Heat engines are fundamental physical objects to develop nonequilibrium thermodynamics. The thermodynamic performance of the heat engine is determined by the choice of cycle and time-dependence of parameters. Here, we propose a systematic numerical method to find a heat engine cycle to optimize some target functions. We apply the method to heat engines with slowly varying parameters and show that the method works well. Our numerical method is based on the genetic algorithm which is widely applied to various optimization problems.
Certain solutions of Einstein's equations in anti-de Sitter spacetime can be engineered, using extended gravitational thermodynamics, to yield `holographic heat engines', devices that turn heat into useful mechanical work. On the other hand, there are constructions (both experimental and theoretical) where a series of operations is performed on a small quantum system, defining what are known as `quantum heat engines'. We propose that certain holographic heat engines can be considered models of quantum heat engines, and the possible fruitfulness of this connection is discussed. Motivated by fea…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability to observe a transition between two states under the forward and the time reversed dynamics, and leads, as in the classical case, to fluctuation relations as tautological identities. As in classical dynamics in contact with a heat bath, time reversal is not unique, and we discuss several possibilities. For any bistochastic map its dual map preserves the trace…
We propose a quantum-enhanced heat engine with entanglement. The key feature of our scheme is superabsorption, which facilitates enhanced energy absorption by entangled qubits. Whereas a conventional engine with $N$ separable qubits provides power with a scaling of $P = Θ(N)$, our engine uses superabsorption to provide power with a quantum scaling of $P = Θ(N^2)$. This quantum heat engine also exhibits a scaling advantage over classical ones composed of $N$-particle Langevin systems. Our work elucidates the quantum properties allowing for the enhancement of performance.
In this paper, we study the role and relevance of the cost for an invariant-based shortcut to adiabaticity enabled qubit heat engine operates in a quantum Otto cycle. We consider a qubit heat engine with Landau-Zener Hamiltonian and improve its performance using the Lewis-Riesenfeld invariant-based shortcut to adiabaticity method. Addressing the importance of cost for better performance, the paper explores its relationship with the work and efficiency of the heat engine. We analyze the cost variation with the time duration of non-adiabatic unitary processes involved in the heat engine cycle. T…
Quantum heat engines are expected to outperform the classical counterparts due to quantum coherences involved. Here we experimentally execute a single-ion quantum heat engine and demonstrate, for the first time, the dynamics and the enhanced performance of the heat engine originating from the Liouvillian exceptional points (LEPs). In addition to the topological effects related to LEPs, we focus on thermodynamic effects, which can be understood by the Landau-Zener-Stuckelberg process under decoherence. We witness a positive net work from the quantum heat engine if the heat engine cycle dynamica…
We report an experimental demonstration of a coupled-mode heat engine in a two-membrane-in-the-middle cavity optomechanical system. The normal mode of the cavity-mediated strongly coupled nanoresonators is utilized as the working medium and an Otto cycle is realized by extracting work between two phononic thermal reservoirs. The heat engine performance is characterized in both normal mode and bare mode pictures, which reveals that the correlation of two membranes plays a significant role during the thermodynamic cycle. Moreover, a straight-twin nanomechanical engine is implemented by engineeri…
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…
Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature differences. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We investigate the effects of different heat capacity characteristics of the sources on the heat engine's efficiency at maximum work (EMW) in the quasi-static limit. In addition, we study the…
The heat engine, a machine that extracts useful work from thermal sources, is one of the basic theoretical constructs and fundamental applications of classical thermodynamics. The classical description of a heat engine does not include coherence in its microscopic degrees of freedom. By contrast, a quantum heat engine might possess coherence between its internal states. Although the Carnot efficiency cannot be surpassed, and coherence can be performance degrading in certain conditions, it was recently predicted that even when using only thermal resources, internal coherence can enable a quantu…
