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Communications in Theoretical Physics

Influence of an indefinite causal order on an Otto heat engine

Jifei Zhao, You-Yang Xu

Published Jan 7, 2022• 5 citations
Publisher

Abstract

Abstract The quantum effect plays an important role in quantum thermodynamics, and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention. Based on two trapped ions, we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering. Then, we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one. When the power is its maximum, the efficiency is also much higher than that of a normal Otto heat engine. This enhancement may originate from the non-equilibrium of the reservoir and the measurement on the control qubit.

DOI
10.1088/1572-9494/ac490d

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•Aug 29, 2025•0 citations
Abstract The quantum effect plays an important role in quantum thermodynamics, and recently the application of an indefinite causal order to quantum thermodynamics has attracted much attention. Based on two trapped ions, we propose a scheme to add an indefinite causal order to the isochoric cooling stroke of an Otto engine through reservoir engineering. Then, we observe that the quasi-static efficiency of this heat engine is far beyond the efficiency of a normal Otto heat engine and may reach one. When the power is its maximum, the efficiency is also much higher than that of a normal Otto heat engine. This enhancement may originate from the non-equilibrium of the reservoir and the measurement on the control qubit.
Abstract Recent theoretical and experimental studies in quantum heat engines show that, in the quasi-static regime, it is possible to have higher efficiency than the limit imposed by Carnot, provided that engineered reservoirs are used. The quasi-static regime, however, is a strong limitation to the operation of heat engines, since an infinitely long time is required to complete a cycle. In this paper we propose a two-level model as the working substance to perform a quantum Otto heat engine surrounded by a cold thermal reservoir and a squeezed hot thermal reservoir. Taking advantage of this model we show a striking achievement, that is to attain unity efficiency even at non-null power.
We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.
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.
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 could surpass the Otto limit and even the Carnot limit and the power could be much higher than the rated power. The efficiency anomaly is due to the energy in the initial state. Thus, we suggest that periodically pumping could take the similar role of a hot bath but could be manipulated flexibly. Furthermore, we propose a new quantum engine working in a single reservoir to convert the pump energy into mechanical work. This manipulative engine could potentially be applied to working in the microenvironments without a large temperature difference, such as the biological tissues in vivo. Our protocol is expected to model a new quantum engine with the advantage of applicability and controllability.
The non-equilibrium properties of open quantum systems are determined by the microscopic laws governing energy exchange with their environment. In particular, an enhancement of the performance of quantum heat engines has been predicted by speeding up the dynamics through control of the system--bath interaction. However, direct microscopic control of heat transfer between the machine and the reservoir has remained elusive so far. Here, we experimentally demonstrate such control in a quantum Otto engine realized with ultracold Cs-133 atoms coupled to an atomic reservoir of ultracold Rb-87 atoms. Heat exchange between the two is mediated by inelastic s-wave collisions whose energy-dependent scattering cross sections lead to an asymmetric equilibration dynamics in the isochoric heating and cooling strokes. By tuning the kinetic temperature of the atomic reservoir, we modify the associated microscopic scattering rates, and thereby the heat transfer law, giving control over the time allocation within the engine cycle through control over the microscopic, multi-exponential relaxation dynamics. This enables power output optimization at fixed efficiency. Our results establish microscopic control of system-reservoir interactions as a tool for manipulating heat flow at the nanoscale and engineering the finite-time performance of quantum thermal machines.
Abstract This paper presents an analysis of quantum Otto heat engines operating in non-equilibrium. It explores the fundamental thermodynamic principles that govern these engines, focusing on efficiency, work output, and the impact of environmental factors such as thermal gradients, external fields, noise, and decoherence. The study investigates the effects of non-equilibrium conditions on engine performance, highlighting challenges and opportunities in practical realizations. Through numerical simulations, the article examines the power, efficiency, and performance coefficients, revealing trade-offs between these metrics and the influence of temperature differences and internal coupling strength. The results demonstrate that non-equilibrium effects can significantly reduce efficiency compared to ideal scenarios, emphasizing the importance of considering both quantum effects and real-world limitations in the design and optimization of quantum heat engines. This work contributes to the growing body of knowledge in quantum thermodynamics, offering insights for quantum computing, sustainable energy technologies, and thermodynamic cycles at the quantum scale.