By periodically driving the temperature of reservoirs in a quantum heat engine, geometric or Pancharatnam-Berry phaselike (PBp) effects in the thermodynamics can be observed. The PBp can be identified from a generating function (GF) method within an adiabatic quantum Markovian master equation formalism. The GF is shown not to lead to a standard open quantum system's fluctuation theorem in the presence of phase-different modulations with an inapplicability in the use of large deviation theory. Effect of quantum coherences in optimizing the flux is nullified due to PBp contributions. The linear coefficient, 1/2, which is universal in the expansion of the efficiency at maximum power in terms of Carnot efficiency no longer holds true in the presence of PBp effects.
By periodically driving the temperature of reservoirs in a quantum heat engine, geometric or Pancharatnam-Berry phaselike (PBp) effects in the thermodynamics can be observed. The PBp can be identified from a generating function (GF) method within an adiabatic quantum Markovian master equation formalism. The GF is shown not to lead to a standard open quantum system's fluctuation theorem in the presence of phase-different modulations with an inapplicability in the use of large deviation theory. Effect of quantum coherences in optimizing the flux is nullified due to PBp contributions. The linear coefficient, 1/2, which is universal in the expansion of the efficiency at maximum power in terms of Carnot efficiency no longer holds true in the presence of PBp effects.
In this work we study the effect of quantum and thermal fluctuations on the statistics of quantum heat engine performance parameters, like efficiency and power. We begin by deriving an explicit solution for the characteristic function of the heat distribution of a thermal quantum harmonic oscillator. We then derive a general framework based on the standard two-point-measurement scheme to compute the efficiency distribution of a quantum Otto cycle. We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems. We find that the efficiency is deterministic and that its mean is equal to the macroscopic efficiency for adiabatic driving. We continue our research by studying the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follow the ’universal’ theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We can relate this unusual property to the perfect anticorrelation between work output and heat input that suppresses thermal as well as quantum fluctuations. We then probe our findings in an experimental NMR setup using spin-1/2 systems and find them to agree rather well with our theoretical predictions. Afterward, we move on to the finite-time quantum Carnot cycle and investigate its power fluctuations. In particular, we consider how level degeneracy and level number, two commonly found properties in quantum systems, influence the relative work fluctuations. We find that their optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results highlight that these parameters can be employed to realize high-performance, high-stability cyclic quantum heat engines.
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 discuss whether, and under which conditions, it is possible to realize a heat engine simply by dynamically modulating the couplings between the quantum working medium and thermal reservoirs. For that purpose, we consider the paradigmatic model of a quantum harmonic oscillator, exposed to a minimal modulation, that is, a monochromatic driving of the coupling to only one of the thermal baths. We demonstrate, at any order in the system/bath coupling strength, that in this setup non-Markovianity of the bath is a necessary condition to obtain a heat engine. In addition, we identify suitable structured environments for the engine to approach the ideal Carnot efficiency. Our results open up new possibilities for the use of non-Markovian open quantum systems for the construction and optimization of quantum thermal machines.
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
We present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between different levels can be an obstacle for ideal operation. In quantum systems, the heat flux is decomposed into the population and coherent parts. The coherent part is specific to quantum systems, and in contrast to the population part, it cannot be expressed by a simple series expansion in the linear-response regime. We discuss how the interplay between the population and coherent parts affects the performance of the heat engine.
We consider a recently proposed four-level quantum heat engine (QHE) model to analyze the role of quantum coherences in determining the thermodynamic properties of the engine, such as flux, output power, and efficiency. A quantitative analysis of the relative effects of the coherences induced by the two thermal baths is brought out. By taking account of the dissipation in the cavity mode, we define useful work obtained from the QHE and present some analytical results for the optimal values of relative coherences that maximizes flux (hence output power) through the engine. We also analyze the role of quantum effects in inducing population inversion (lasing) between the states coupled to the cavity mode. The universal behavior of the efficiency at maximum power (EMP) is examined. In accordance with earlier theoretical predictions, to leading order, we find that $\mathrm{EMP}\ensuremath{\sim}{\ensuremath{\eta}}_{c}/2$, where ${\ensuremath{\eta}}_{c}$ is Carnot efficiency. However, the next higher order coefficient is system dependent and hence nonuniversal.