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arXiv:2505.22902 · Physical Review A

Markovian heat engine boosted by quantum coherence

Freddier Cuenca-Montenegro, Marcela Herrera, John Henry Reina

Published Jun 15, 2026• 0 citations
arXivHTMLPDF

Abstract

We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian, one-qubit heat engine. By consuming the coherence of noisy quantum states, we demonstrate that the engine can surpass the classical efficiency limit when operating according to a quantum Otto cycle. The engine's non-classical nature is demonstrated by its violation of the Leggett-Garg's temporal correlations inequality. Amplitude damping increases the extractable work under partial thermalization, thereby increasing the efficiency. In contrast, phase damping increases the extractable work under partial thermalization but reduces the efficiency. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost to establish a direct link between energy consumption and information processing in quantum heat engines.

DOI
10.1103/hpkj-srj6

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We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian, one-qubit heat engine. By consuming the coherence of noisy quantum states, we demonstrate that the engine can surpass the classical efficiency limit when operating according to a quantum Otto cycle. The engine's non-classical nature is demonstrated by its violation of the Leggett-Garg's temporal correlations inequality. Amplitude damping increases the extractable work under partial thermalization, thereby increasing the efficiency. In contrast, phase damping increases the extractable work under partial thermalization but reduces the efficiency. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost to establish a direct link between energy consumption and information processing in quantum heat engines.
Quantum thermodynamics studies quantum effects in thermal machines. Both quantum coherence and quantum correlations have been theoretically shown to be a physical resource able to boost their performance. But when is a heat engine, which cyclically interacts with external reservoirs that unavoidably destroy its phase coherence, really quantum? We here use the Leggett-Garg inequality to assess the nonclassical properties of a paradigmatic two-level Otto engine with quantum friction. We provide the complete phase diagram characterizing the quantumness of the engine as a function of its parameters and distinguish three different phases: a quantum phase separated from a classical phase by a transition regime. We further derive an analytical expression for the quantum-to-classical transition temperature.
Abstract We identify that quantum coherence is a valuable resource in the quantum heat engine, which is designed in a quantum thermodynamic cycle assisted by a quantum Maxwell’s demon. This demon is in a superposed state. The quantum work and heat are redefined as the sum of coherent and incoherent parts in the energy representation. The total quantum work and the corresponding efficiency of the heat engine can be enhanced due to the coherence consumption of the demon. In addition, we discuss an universal information heat engine driven by quantum coherence. The extractable work of this heat engine is limited by the quantum coherence, even if it has no classical thermodynamic cost. This resource-driven viewpoint provides a direct and effective way to clarify the thermodynamic processes where the coherent superposition of states cannot be ignored.
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.
In this article we use optimal control to maximize the efficiency of a quantum heat engine executing the Otto cycle in the presence of external noise. We optimize the engine performance for both amplitude and phase noise. In the case of phase damping we additionally show that the ideal performance of a noiseless engine can be retrieved in the adiabatic (long time) limit. The results obtained here are useful in the quest for absolute zero, the design of quantum refrigerators that can cool a physical system to the lowest possible temperature. They can also be applied to the optimal control of a collection of classical harmonic oscillators sharing the same time-dependent frequency and subjected to similar noise mechanisms. Finally, our methodology can be used for the optimization of other interesting thermodynamic processes.
Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.
With the development of any quantum technology comes a need for precise control of quantum systems. Here, we evaluate the impact of control noise on a quantum Otto cycle. While it is postulated that noiseless quantum engines can approach maximal Otto efficiency in finite times, the existence of white noise on the controls is shown to negatively affect average engine performance. Two methods of quantum enhancement, counterdiabatic driving and quantum lubrication, are implemented and found to improve the performance of the noisy cycle only in specified parameter regimes. To gain insight into performance fluctuations, projective energy measurements are used to construct a noise-averaged probability distribution without assuming full thermalization or adiabaticity. From this, the variances in thermodynamic currents are observed to increase as average power and efficiency improve, and are also shown to be consistent with known bounds from thermodynamic uncertainty relations. Lastly, by comparing the average functioning of the unmonitored engine to a projectively measured engine cycle, the role of coherence in work extraction for this quantum engine model is investigated.