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arXiv:2509.04901

Power-efficiency-stability trade-off in quantum information engines

Milton Aguilar, Cüneyt Ünal, Eric Lutz

Published Sep 5, 2025• 0 citations
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Abstract

Efficiency and power are two central measures of the performance of thermal machines. We here study the power-efficiency-stability trade-off in a finite-time quantum Carnot information engine, in which an information reservoir replaces the usual cold bath of a quantum Carnot engine. We analytically evaluate mean and variance of the work output, and demonstrate that maximum efficiency can be reached at both finite work output and finite work output fluctuations. We additionally show that the relative work output fluctuations may be smaller than those of the corresponding Carnot heat engine. This result implies that the finite-time quantum Carnot information engine can be more stable than the quantum Carnot heat engine, an important property for practical applications.

DOI
10.48550/arxiv.2509.04901

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Efficiency and power are two central measures of the performance of thermal machines. We here study the power-efficiency-stability trade-off in a finite-time quantum Carnot information engine, in which an information reservoir replaces the usual cold bath of a quantum Carnot engine. We analytically evaluate mean and variance of the work output, and demonstrate that maximum efficiency can be reached at both finite work output and finite work output fluctuations. We additionally show that the relative work output fluctuations may be smaller than those of the corresponding Carnot heat engine. This result implies that the finite-time quantum Carnot information engine can be more stable than the quantum Carnot heat engine, an important property for practical applications.
We study the efficiency at maximum power, ${\ensuremath{\eta}}_{m}$, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ${\ensuremath{\eta}}_{m}$ becomes identical to the Carnot efficiency ${\ensuremath{\eta}}_{{}_{C}}=1\ensuremath{-}{T}_{c}/{T}_{h}$. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ${\ensuremath{\eta}}_{m}$ at maximum power output is bounded from above by ${\ensuremath{\eta}}_{{}_{C}}/(2\ensuremath{-}{\ensuremath{\eta}}_{{}_{C}})$ and from below by ${\ensuremath{\eta}}_{{}_{C}}/2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ${\ensuremath{\eta}}_{{}_{\mathit{CA}}}=1\ensuremath{-}\sqrt{{T}_{c}/{T}_{h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot measurements. The engines operate in a one-step cycle by letting the working system simultaneously interact with hot and cold baths via semilocal thermal operations. By allowing quantum entanglement between its constituents and, thereby, a coherent transfer of heat from hot to cold baths, the engine implements the fastest possible reversible state transformation in each cycle, resulting in maximum power and Carnot efficiency. Finally, we propose a physically realizable engine using quantum optical systems.
We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures ${\ensuremath{\beta}}_{h}$ and ${\ensuremath{\beta}}_{c}(>{\ensuremath{\beta}}_{h})$ with $({k}_{B}\ensuremath{\equiv}1)\ensuremath{\beta}=1/T$. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as ${\ensuremath{\eta}}_{mp}={({\ensuremath{\eta}}_{C}^{\mathrm{gen}})}^{2}/[{\ensuremath{\eta}}_{C}^{\mathrm{gen}}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})]$, where the generalized Carnot efficiency ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}$ in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter $\ensuremath{\gamma}$: ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}=1\ensuremath{-}{\ensuremath{\beta}}_{h}/[{\ensuremath{\beta}}_{c}cosh(2\ensuremath{\gamma})]$. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.
Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.
We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine model with a two-level spin as the working medium. It mimics a low dissipation engine as confirmed by finite time thermodynamic optimization results. The so-obtained EMP, being constrained by the generalized bounds, is well described by a generalized Curzon- Ahlborn efficiency as consequences of a left/right symmetry for a rate constant and low dissipations. Intriguing features of this minimal heat engine under optimal power output are also demonstrated.
A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.