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arXiv:2607.01811

Extracting Work from Discrete Quantum Polytropic Processes

Vishal Anand, Swarup Kumar Giri, Avijit Misra, Subhadip Mitra, Samyadeb Bhattacharya

quant-phSubmitted Jul 2, 2026• Announced Jul 3, 2026
arXivHTMLPDF

Abstract

We establish an upper bound on extractable work for time-dependent, non-Markovian quantum heat engines operating with finite baths. This bound analytically isolates the distinct thermodynamic penalties arising from system-bath correlations, bath non-equilibrium, and residual interaction energy. Evaluating this framework operationally via a quantum polytropic cavity-optomechanical cycle, we demonstrate that maximal efficiency requires quasi-static operation to successfully harvest coherent, non-Markovian system-bath resonances. Conversely, optimising for maximum power enforces a strict finite-time regime. Under realistic hardware constraints, this acceleration necessitates larger discrete operational steps, where we expect Trotterisation errors to manifest as physical noise. Such noise would irreversibly suppress delicate quantum memory effects, forcing a collapse to the memoryless Markovian Otto limit. Coupled with the permanent energetic tax of switching finite-bath interactions, our results indicate that the exploitation of quantum memory resources and finite-power operation belong to different operational regimes.

Comments
12 pages, 7 figures. Comments are welcome

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We establish an upper bound on extractable work for time-dependent, non-Markovian quantum heat engines operating with finite baths. This bound analytically isolates the distinct thermodynamic penalties arising from system-bath correlations, bath non-equilibrium, and residual interaction energy. Evaluating this framework operationally via a quantum polytropic cavity-optomechanical cycle, we demonstrate that maximal efficiency requires quasi-static operation to successfully harvest coherent, non-Markovian system-bath resonances. Conversely, optimising for maximum power enforces a strict finite-time regime. Under realistic hardware constraints, this acceleration necessitates larger discrete operational steps, where we expect Trotterisation errors to manifest as physical noise. Such noise would irreversibly suppress delicate quantum memory effects, forcing a collapse to the memoryless Markovian Otto limit. Coupled with the permanent energetic tax of switching finite-bath interactions, our results indicate that the exploitation of quantum memory resources and finite-power operation belong to different operational regimes.
Abstract We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.
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 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.
We show that frequent nondemolition measurements of a quantum system immersed in a thermal bath allow the extraction of work in a closed cycle from the system-bath interaction (correlation) energy, a hitherto unexploited work resource. It allows for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time. The predicted work resource may be the basis of quantum engines embedded in a bath with long memory time, such as the electromagnetic bath of a high-QQQ cavity coupled to two-level systems.
We derive a bound on the efficiency of thermal engines that can be sharper than Carnot's limit. It is a function of statistical correlations between the engine internal state and Hamiltonian, can be saturated even in finite-time cycles, and applies to both classical and quantum engines. Specifically, the bound establishes the exact maximal efficiency of engines operating with multiple baths, tightening the upper limit set by Carnot's theorem. Then, we show that an engine made of a quantum dot coupled with fermionic baths can achieve the bound, even when operating beyond the quasistatic regime. The result provides a design principle for realistic energy harvesting machines.
Abstract Quantum heat engines (QHEs) are commonly believed to achieve their optimal efficiency only when operated quasi-statically. When running at finite power, however, they suffer effective friction due to the generation of coherences and transitions between energy eigenstates. It was noted that it is possible to increase the power of a QHE using external control schemes or suitable dephasing noise. Here, we investigate the thermodynamic cost associated with dephasing noise schemes using both numerical and analytical methods. Our findings unveil that the observed gain in power is generally not free of thermodynamic costs, as it involves energy costs of the control fields or heat flows between thermal and dephasing baths. These contributions must be duly accounted for when determining the engine’s overall efficiency. We identify suitable regimes in which, at a fixed effective dephasing rate, the heat leaked into the explicitly modelled dephasing bath can be made arbitrarily small, so that the efficiency at finite power approaches that of a quasi-statically operated Otto engine even when the dephasing environment is fully accounted for.