To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions.
We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperature after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations and…
We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-dr…
From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $Δ$, and a careful distinction between the Gibbs relation $dE = T dS + (E/Δ) dΔ$ and the energy balance equation $dE = δQ^\leftarrow - δW^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $Δ$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with …
The stochastic efficiency [G. Verley et al., Nat. Commun. 5, 4721 (2014)] was introduced to evaluate the performance of energy-conversion machines in micro-scale. However, such an efficiency generally diverges when no heat is absorbed while work is produced in a thermodynamic cycle. As a result, any statistical moments of the efficiency do not exist. In this study, we come up with a different version of the definition for the stochastic efficiency which is always finite. Its mean value is equal to the conventional efficiency, and higher moments characterize the fluctuations of the cycle. In ad…
We construct an entangled quantum Otto engine based on spin-1/2 systems undergoing Dzyaloshinski-Moriya (DM) interaction within a varying magnetic field. We investigate the influence of the DM interaction on basic thermodynamic quantities, including heat transfer, work done, and efficiency and find that the DM interaction importantly influences the engine's thermodynamics. We obtain an expression for engine efficiency, finding it to yield the same efficiency for antiferromagnetic and ferromagnetic coupling. A new upper bound, nontrivially consistent with the second law of thermodynamics, is de…
The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling betwee…
We study a four-stroke Otto engine whose working fluid is a quantum Ising chain. The thermodynamic cycle consists in sweeps of the transverse magnetic field occurring in thermal isolation, alternated by thermalisation strokes with reservoirs at different temperatures. The system-environment coupling is modelled in a thermodynamically consistent way by means of a nonlocal Lindblad master equation. We show that the engine may operate in four different operation modes, depending on the various parameters, in particular it can act as a heat engine and as a refrigerator. We detect an enhancement of…
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 maxim…
We investigate a heat engine with a finite length Kitaev chain in an Otto cycle. Finite size effects are taken into account using method of Hill's nano-thermodynamics as well as using the method of temperature dependent energy levels. We distinguish the bulk and boundary contributions to the efficiency and the work output of Kitaev chain engine and identify them as non-Otto heat engine and refrigerator cycles, respectively. Possibility of separately running Otto engine cycles associated with the bulk and the whole system, and an Otto refrigerator at the boundary is pointed out. It is found tha…
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cyc…
We study a limit cycle of a quantum Otto engine whose each cycle consists of two finite-time quantum isochoric (heating or cooling) processes and two quantum adiabatic work-extracting processes. Considering a two-level system as a working substance that weakly interacts with two reservoirs comprising an infinite number of bosons, we investigate the non-Markovian effect (short-time behavior of the reduced dynamics in the quantum isochoric processes (QIPs)) on work extraction after infinite repetition of the cycles. We focus on the parameter region where energy transferred to the reservoir can c…
Quantum thermodynamics studies quantum effects in thermal machines. But when is a heat engine, which cyclically interacts with external reservoirs that unavoidably destroy its quantum coherence, really quantum? We here use the Leggett-Garg inequality to assess the nonclassical properties of a single two-level Otto engine. We provide the complete phase diagram characterizing the quantumness of the engine as a function of its parameters and identify three distinct phases. We further derive an explicit expression for the transition temperature.
Gauge-invariant thermodynamics of a finite-time quantum Otto engine
Institute of Physics, Federal University of Goiás（戈亚斯联邦大学物理研究所）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Instituto de Física de São Carlos, Universidade de São Paulo（圣保罗大学圣卡洛斯物理研究所）
We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show th…
In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction'. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the…
The quantum heat engines have drawn much attention due to miniaturization of devices recently. We study the dynamics of the quantum Otto heat engine using the driven-dissipative Schrödinger equation. Starting from different initial states, we simulate the time evolutions of the internal energy, power and heat-work conversion efficiency. The initial state impacts on these thermodynamic quantities before the Otto cycle reaches stable. In the transition period, the efficiency and power may be higher or lower than the corresponding values in the cyclostationary state. Remarkably, the efficiency co…
We investigate a quantum heat engine with a working substance of two particles, one with a spin $1/2$ and the other with an arbitrary spin (spin $s$), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin $s$ on the work output and the thermal eff…
We introduce a quantum heat engine performing an Otto cycle by using the thermal properties of the quantum vacuum. Since Hawking and Unruh, it has been established that the vacuum space, either near a black hole or for an accelerated observer, behaves as a bath of thermal radiation. In this work, we present a fully quantum Otto cycle, which relies on the Unruh effect for a single quantum bit (qubit) in contact with quantum vacuum fluctuations. By using the notions of quantum thermodynamics and perturbation theory we obtain that the quantum vacuum can exchange heat and produce work on the qubit…
We consider a quasi-static quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength $J>0$, in the presence of an external magnetic field $B$ which is varied during the cycle. We prove the positive work condition, and show that level-degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than from the non-degenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as…
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 …
We introduce quantum heat engines that perform quantum Otto cycle and the quantum Stirling cycle by using a coupled pair of harmonic oscillator as its working substance. In the quantum regime, different working medium is considered for the analysis of the engine models to boost the efficiency of the cycles. In this work, we present Otto and Stirling cycle in the quantum realm where the phase space is non-commutative in nature. By using the notion of quantum thermodynamics we develop the thermodynamic variables in non-commutative phase space. We encounter a catalytic effect (boost) on the effic…
To optimize the performance of a heat engine in finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a \mathcal{C}/τ^{2} scaling for long control time τ. There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work can not be neglected in some quantum systems with simple energy-level stru…
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…
We study a driven harmonic oscillator operating an Otto cycle between two thermal baths of finite size. By making extensive use of the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths' standpoint. For sufficiently large baths, our engine is capable of running a number of ideal cycles, delivering finite power while operating very…
The Filtering Demon: Beyond Standard Thermodynamic Bounds and Harnessing Measurement Error and Quantum Friction
College of Physics, Jilin University（吉林大学物理学院）；Department of Chemistry and Department of Physics and Astronomy, State University of New York at Stony Brook（纽约州立大学石溪分校化学系和物理与天文学系）
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…
Quantum thermal machines make use of non-classical thermodynamic resources, one of which is 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 earlier shown that the said interaction provides an enhancement of cycle efficiency for two spin-1/2 particles, with an upper bound which is tighter than the Carnot efficiency. However, the necessary conditions g…
Cross-Spectral Reservoir Correlations as a Resource for Finite-Time Quantum Otto Engines
Ramakrishna Mission Vivekananda Educational and Research Institute（拉马克里希纳使命维韦卡南达教育研究所）；TCG CREST；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）
Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We es…
We discuss a model of a closed quantum evolution of two-qubits where the joint Hamiltonian is so chosen that one of the qubits acts as a bath and thermalize the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients, representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic pro…
Interesting effects arise in cyclic machines where both heat and ergotropy transfer take place between the energising bath and the system (the working fluid). Such effects correspond to unconventional decompositions of energy exchange between the bath and the system into heat and work, respectively, resulting in efficiency bounds that may surpass the Carnot efficiency. However, these effects are not directly linked with quantumness, but rather with heat and ergotropy, the likes of which can be realised without resorting to quantum mechanics.
According to Clausius formulation of the second law of thermodynamics, for any thermal machine withdrawing heats $Q_{1,2}$ from two heat reservoirs at temperatures $T_{1,2}$, it holds $Q_1/T_1+Q_2/T_2 \leq 0$. Combined with the observation that the quantity $Q_1+Q_2$ is the work $W$ done by the system, that inequality tells that only 4 possible operation modes are possible for the thermal machine, namely heat engine [E], refrigerator [R], thermal accelerator [A] and heater [H]. We illustrate their emergence in the finite time operation of a quantum Otto engine realised with a single qubit. We …
