Efficiency fluctuations in quantum heat engines with non-quasi-static adiabatic strokes

arXiv:2610.10647 · cond-mat.stat-mech, cond-mat.quant-gas · Submitted 2026-10-07 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Efficiency fluctuations in quantum heat engines with non-quasi-static adiabatic strokes".

Mira: The gist: The study analytically and numerically determines efficiency fluctuations in quantum Carnot and Otto engines operating under non-quasi-static adiabatic strokes with quasi-static isothermal or isochoric processes,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're looking at this paper, "Efficiency fluctuations in quantum heat engines with non-quasi-static adiabatic strokes," and what it claims is that when you run these engines, especially the Carnot and Otto types, with pistons moving faster than allowed by the slow process assumption, you get extra quantum noise that changes how efficient they are.

Mira: That’s right, Kai. The main idea here is looking at how the work output becomes random because of this non-quasi-static motion during those expansion and compression strokes—the adiabatic ones specifically—and how that randomness modifies the average efficiency we calculate.

Lev: From an error correction standpoint, if you were trying to run this on actual hardware, that means you're dealing with stochastic work outputs W1 and W2, which aren't just fixed numbers anymore, and that makes characterizing the noise a real headache for building stable systems forty-two <ref:2610.10647#pg2>.

Kai: Exactly. The paper models each piston as a single particle in a one-dimensional box with a moving wall, making the whole system's Hamiltonian time-dependent, which drives these quantum transitions during those non-equilibrium strokes forty-three <ref:2610.10647#pg2,a single particle in a>.

Mira: And they use this two-point measurement scheme just on the adiabatic strokes to find the efficiency distribution that includes both thermal and these new quantum fluctuations. The paper states that for an adiabatic stroke of finite duration, those quantum fluctuations actually dominate the thermal ones when you have a small piston size and low temperature <ref:2610.10647#pg3>.

Lev: That leads to some interesting numbers they show; they find that work done during these non-quasi-static strokes, W1 and W2, can actually take values outside the classical bounds of zero to one, meaning efficiencies eta n,m,j,k can be anything between zero and one <ref:2610.10647#pg2>.

Kai: So the key thing they find is that this randomness in W1 and W2 is what modifies the average efficiency calculation for both the Carnot engine and the Otto engine <ref:2610.10647#pg3>.

Mira: They define efficiency for these engines as a specific combination of work done during those strokes divided by the heat absorbed or rejected, like eta n,m,j,k = W¯ DA(Th) + W1 + W¯ BC (Tc) + W2 / Q¯ h <ref:2610.10647#pg3>.

Lev: The paper also points out that the probability distribution function for those work outputs P(W1, W2) is useful because it lets you figure out the distribution of the final efficiency for the Carnot engine <ref:2610.10647#pg3>.

Kai: When they look at the average efficiency in a quasi-static limit, say when piston speed goes to zero and time goes to infinity, they get a result that looks like eta¯qs = one - Q¯ c / Q¯ h <ref:2610.10647#pg3>.

Mira: That quasi-static average efficiency is what you'd expect classically, but the paper shows how the oscillations in that mean efficiency come specifically from those additional quantum fluctuations driven by the piston's motion that only disappear when you look at very large lengths <ref:2610.10647#pg3>.

Lev: If we take this to real hardware, it means your measured average efficiency won't just be one smooth number; it will have these quantum jitters that depend on the scale of the piston motion <ref:2610.10647#pg3>.

Kai: So what this means for us in the lab is that if we’re working at mesoscopic scales, this study gives us a way to predict how much noise we should expect when we run those non-quasi-static strokes <ref:2610.10647#pg1>.

Mira: It opens up the discussion for larger systems too, because the authors mention that these findings could be generalized if you consider many-particle systems as working substances, although they admit that this is an open problem <ref:2610.10647#pg3>.

Lev: And what’s missing, which they flag as a limitation, is the fact that they assumed quasi-static processes for those non-adiabatic strokes; if you introduce actual heat input fluctuations into those strokes, that's something we haven't fully settled yet <ref:2610.10647#pg3>.

Kai: So, to wrap up this segment, the paper "Efficiency fluctuations in quantum heat engines with non-quasi-static adiabatic strokes" shows that piston speed introduces extra quantum noise into the work done during expansion and compression <ref:2610.10647#pg1>.

Mira: It's showing us how these engines behave when you push them beyond the slow, quasi-static limits, revealing efficiency fluctuations that are driven by the underlying quantum mechanics of the piston's motion <ref:2610.10647#pg2>.

Lev: And for those trying to build stable engines, it highlights that you have to account for these stochastic outputs W1 and W2 because they aren't just classical inputs anymore <ref:2610.10647#pg3>.

Conclusion: Kai: So we’re looking at this paper, "Efficiency fluctuations in quantum heat engines with non-quasi-static adiabatic strokes," and what it really boils down to is that when you run these quantum Carnot and Otto engines, especially when the piston moves too fast for a slow process, you get extra noise.

Mira: Right. The core idea is that those rapid movements introduce stochastic work—random work output—which messes with our standard efficiency calculations. We're seeing how thermal effects mix with these new quantum fluctuations during the expansion and compression strokes.

Lev: From my side, that means if you try to build this on real hardware, those W1 and W2 values aren't fixed numbers anymore; they're probability distributions, which makes designing anything stable much harder.

Kai: So the paper says that by modeling each piston as a particle in a box with a moving wall, they can actually get these efficiency distributions for both engine types.

Mira: They show that for those non-quasi-static adiabatic strokes, quantum fluctuations end up dominating the thermal ones when you have small pistons and low temperatures. That means the efficiency isn't just one smooth value anymore; it has multiple sharp peaks at different possible values.

Lev: I saw that they found work outputs W1 and W2 can actually go outside the classical bounds of zero to one, which is a weird thing for an efficiency measure.

Kai: So what this changes for us in the lab is that if we’re working at mesoscopic scales, we have to account for these jitters when predicting how well our engines will actually perform.

Mira: It suggests that even in these relatively simple heat engines, the underlying quantum mechanics of piston motion has a measurable impact on the final efficiency statistics.

Lev: And while they use quasi-static assumptions for those strokes, the paper points out that if you actually include heat input fluctuations during those strokes, that’s something they haven't fully tackled yet.

Kai: It’s interesting because it shows how pushing a system beyond its slow limit reveals these hidden quantum effects in the performance of things we think are pretty well understood.

School of Physics, University of Hyderabad

cond-mat.stat-mech, cond-mat.quant-gas

Submitted: 2026-10-07

Updated: 2026-10-07

Comments: 11 pages, 6 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: The gist: The study analytically and numerically determines efficiency fluctuations in quantum Carnot and Otto engines operating under non-quasi-static adiabatic strokes with quasi-static isothermal

Key concepts

Non-quasi-static adiabatic strokes: These are the expansion and compression phases of the engine where the piston moves too quickly for a standard, slow process. The study models this by treating each piston as a quantum particle in a box with a moving wall, leading to time-dependent quantum mechanical transitions.
Quantum fluctuations: These are unpredictable variations in work output caused by the fundamental nature of quantum mechanics. In this engine analysis, these fluctuations arise specifically from the motion of the piston during non-quasi-static strokes and can cause efficiency to vary significantly.
Two-point measurement scheme: This is a specific method used in the research to determine transition probabilities between different energy states during the adiabatic strokes. It helps quantify how quantum mechanical changes occur when the piston moves, allowing researchers to calculate efficiency distributions.

Terminology

Cluster expansion — 1× in this paper · explained in 2 episodes
Energy Efficiency — 1× in this paper · explained in 3 episodes

Summary

The gist: The study analytically and numerically determines efficiency fluctuations in quantum Carnot and Otto engines operating under non-quasi-static adiabatic strokes with quasi-static isothermal or isochoric processes, revealing that piston speed introduces additional quantum fluctuations that modify average engine efficiencies.

Theoretical Framework

The research investigates the stochastic nature of work output resulting from the unitary evolution of the quantum mechanical state during non-equilibrium processes by considering each piston as a single quantum particle in a 1-D box with a non-quasi-statically movable boundary The system is modeled using an infinite square well potential with a moving wall where the Hamiltonian becomes time-dependent, driving quantum mechanical transitions via unitary evolution during the strokes The adiabatic expansion and compression strokes are analyzed using a two-point measurement scheme to determine transition probabilities between energy eigenstates

Quantum Carnot Engine Analysis

The quantum Carnot engine operates through non-quasi-static adiabatic expansion and compression strokes followed by quasi-static isothermal or isochoric strokes The two-point measurement scheme is applied only to the adiabatic expansion and compression strokes, yielding a general expression for the efficiency distribution that incorporates both thermal fluctuations and quantum fluctuations For an adiabatic stroke of finite duration, quantum fluctuations dominate thermal fluctuations when the piston size is small and the temperature is low, resulting in multiple infinitesimally narrow peaks of significant height at discrete efficiency values The work done during the non-quasi-static adiabatic strokes, W1 and W2, becomes stochastic due to the arbitrariness in the choice of quantum numbers and can take values beyond the classical bound 0 ≤ ηn,m,j,k ≤ 1 The efficiency of the quantum Carnot engine is defined as ηn,m,j,k = W¯ DA(Th) + W1 + W¯ BC (Tc) + W2 / Q¯ h

Quantum Otto Engine Analysis

The quantum Otto engine utilizes non-quasi-static adiabatic expansion and compression strokes followed by quasi-static isochoric strokes The relevant processes determining the efficiency include the isochoric quasi-static combustion process, non-quasi-static unitary expansion, isochoric quasistatic heat rejection, and non-quasi-static unitary compression The stochastic work done during these strokes (W1 and W2) in the quantum Otto engine are individually the same as that for the quantum Carnot engine The probability distribution function for the stochastic work outputs P(W1, W2) is useful to determine the probability distribution for the efficiency of the quantum Carnot engine

Efficiency Distribution and Averages

The normalized efficiency distribution function P(η) is derived by integrating over all possible outcomes of the two-point measurements, incorporating all four Boltzmann probabilities and corresponding quantized energy eigenvalues The average efficiency for the quantum Carnot engine in the quasi-static limit (v → 0, τ → ∞, vτ = f inite) takes the form η¯qs = 1 − Q¯ c / Q¯ h Similarly, the average efficiency for the quantum Otto engine also takes a form that is independent of piston size only in the classical limit The oscillations in the mean efficiency stem from the additional effect of quantum fluctuations driven by the piston’s motion, which dies out at large length scales

Conclusion

The findings are useful for Carnot and Otto engines at mesoscopic scales The results can be generalized by considering many-particle systems as working substances, leaving this as an open problem While the study assumed quasi-static processes for non-adiabatic strokes, considering non-quasi-static cases would introduce heat input fluctuations, which remains an open problem The paper concludes by showing that the average efficiency of both quantum engines can be obtained from Eqn. (21).

Improvements for AI systems

No-Piston Quantum Simulation: The AI system can accurately model efficiency fluctuations in quantum heat engines operating with non-quasi-static adiabatic strokes by treating each piston as a single quantum particle in a 1-D box with a non-quasi-statically movable boundary. This allows the system to capture the unitary evolution of the quantum mechanical state of the system during non-equilibrium processes and explicitly shows how the piston speed during quantum non-equilibrium strokes introduces additional quantum fluctuations that modify the average efficiency of both the engines.
Stochastic Efficiency Prediction: The AI can predict a probability distribution function for engine efficiency, as described by Equation (15), by calculating "P(η) = X

e−En(l0)

kBTh

Zl0(Th)

e−Em(lτ)kBTc

Zlτ(Tc)

e−Ej(l′′)kBTc

Zl′''(Tc)e−Ek(l'0)kBTh/Zl'0(Th) which incorporates all the four Boltzmann probabilities and the corresponding quantized energy eigenvalues in Eqn. (14)."

Quantum Engine Parameter Optimization: The system can optimize engine performance by tuning piston speed and stroke duration to maximize or minimize efficiency, as shown in Section 2E and Section 3, where it determine[s] the average efficiency of the quantum Carnot engine for its different piston speeds and analyzes it for the Otto engine.
Classical Limit Transition Modeling: The AI can accurately model the transition between quantum and classical behavior by analyzing how the average efficiency (Eqn. (17)) of the quantum Carnot engine in the quasi-static limit, takes the same form for both engines, and noting that this efficiency takes the well-known form η¯qs ≃ 1 − Tc/Th only in the classical regime.
Mesoscopic Scale Performance Analysis: The AI can evaluate performance metrics specifically at mesoscopic scales, as the study is designed to capture the effect of quantum fluctuations on their efficiencies for engines operating with non-quasi-static adiabatic strokes and operating under conditions where these effects are most pronounced.

Abstract

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.