We propose and analyze the theoretical model for a two-stroke quantum heat engine with one of the heat baths replaced by a non-selective quantum measurement. We show that the engine's invariant reference state depends on whether the cycle is monitored or unmonitored via diagnostic measurements to determine the engine's work output. We explore in detail the average work output and fluctuations of the proposed heat engine for the monitored and unmonitored cases. We also identify unitary work strokes for which the invariant states can support coherences in the energy basis leading to differing predictions for the average energy change during the unitary work strokes and the average work from the standard two-projective measurement approach.
We propose and analyze the theoretical model for a two-stroke quantum heat engine with one of the heat baths replaced by a non-selective quantum measurement. We show that the engine's invariant reference state depends on whether the cycle is monitored or unmonitored via diagnostic measurements to determine the engine's work output. We explore in detail the average work output and fluctuations of the proposed heat engine for the monitored and unmonitored cases. We also identify unitary work strokes for which the invariant states can support coherences in the energy basis leading to differing predictions for the average energy change during the unitary work strokes and the average work from the standard two-projective measurement approach.
A four-stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions, such as different speeds of the work strokes, different temperatures of the heat bath, and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is analyzed. A comparison with a two-temperature Otto engine is provided in the particular case of adiabatic work and ideal thermalization strokes.
This paper investigates a coupled two-qubits heat engine fueled by generalized measurements of the spin components and using a single heat reservoir as sink. Our model extends the proposal of Yi, Talkner, and Kim [Phys. Rev. E 96, 022108 (2017)2470-004510.1103/PhysRevE.96.022108], where the role of a hot reservoir in a four-stroke cycle was replaced by a quantum measurement apparatus, the other steps being two quantum adiabatic strokes and thermalization with a cold reservoir. We propose a five-stroke cycle, where an ergotropy extracting stroke is introduced following the measurement stroke, and study the effect of measurements of different spin components on the performance of the machine. For measurements along z-z directions, we find two possible occupation distributions that yield an active state and the ergotropic stroke improves the performance of the engine over the four-stroke cycle. Further, the three-stroke engine (without the adiabatic strokes) yields the same performance as the five-stroke engine. For arbitrary working medium and nonselective measurements, we prove that the total work output of a five-stroke engine is equal to the sum of the work outputs of the corresponding four-stroke and three-stroke engines. For measurement directions other than z-z, there may be many possible orderings of the postmeasurement probabilities that yield an active state. However, as we illustrate, for specific cases (e.g., x-x), a definite ordering may be obtained with the projective measurements. Thus we find that the five-stroke engine exploiting ergotropy outperforms both its four-stroke as well as three-stroke counterparts.
Quantum heat engines, compared to their classical counterparts, offer many advantages due to quantum effects. The study of different cycle modes contributes to the improvement of heat engine efficiency. In this paper, based on a quantum hybrid heat engine, we compare three cycle modes involving Bell-type quantum weak measurement (without observing the results) and two heat baths at different temperatures, where quantum weak measurements play the role of heat source. Thus, there are two types of heat sources and three processes involving heat absorption or release in our model. In other words, we study a multi-stroke quantum hybrid heat engine. Moreover, we further investigate three types of cycle modes using a working substance composed of a three-particle XXZ spin chain. In the adiabatic stroke, we select three Hamiltonian parameters and vary them adiabatically from their initial to final values, comparing their effects on engine efficiency. In particular, we examine how the ordering of the weak-measurement stroke and the adiabatic stroke influences heat absorption, heat release, and engine efficiency. Additionally, we analyze the impact of the high-temperature bath’s temperature and the weak-measurement strength on the engine efficiency.
Recently, we have considered a single-qubit quantum Otto cycle based on arbitrary (non-unitary) unital channels as a heat source. We showed similarly to some works in literature that the ratio of the fluctuations of work (W) and heat absorbed (QM) is lower-and-upper bounded. In this paper, we drive this line of research further and consider the fluctuations of the stochastic heat exchanged (denoted by QC′) with the cold bath. In general, there is another stochastic quantity, which we denote by QC, that gives the same average as QC′− but not higher cumulants. While QC′ is defined through the two-point measurement scheme, i.e., by measuring the energy of the working medium in all four strokes, QC follows from imposing the first of thermodynamics at the stochastic level. Our work has two important results: (i) first, we prove that the measurement of the working medium during three strokes is sufficient to construct the distribution of QC′ (ii) and that the cumulants of the stochastic entropy production denoted by Σ can be inferred from the cumulants of QC.
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 have presented an analytical and numerical study of efficiency fluctuations in quantum Carnot and Otto engines with pistons operating under non-quasi-static adiabatic expansion and compression processes at constant speed, along with quasi-static isothermal (for the Carnot engine) or isochoric processes (for the Otto engine). We have considered the two-point measurement scheme during the adiabatic strokes in this regard. By considering each of the pistons as a single quantum particle in a 1-D box with a non-quasi-statically movable boundary, we capture the stochastic nature of the work output resulting from the unitary evolution of the quantum mechanical state of the system during non-equilibrium processes. Furthermore, we have explicitly shown how the piston speed during quantum non-equilibrium strokes introduces additional quantum fluctuations that modify the average efficiency of both the engines.