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arxiv: 2303.14619 · v1 · pith:UOQRKKLKnew · submitted 2023-03-26 · 🪐 quant-ph · cond-mat.stat-mech

Finite-Time Optimization of Quantum Szilard heat engine

Tan-Ji Zhou , Yu-Han Ma , C. P. Sun This is my paper

Pith reviewed 2026-05-24 09:19 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords quantum Szilard enginefinite timeMaxwell demonmutual informationLandauer principlequantum thermodynamicsheat engine
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The pith

A finite-time quantum Szilard engine has efficiency bounded by the mutual information from the demon's measurement.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines a quantum Szilard engine operating with a spin particle as working substance where a Maxwell's demon performs a finite-time measurement of the spin state. The efficiency is shown to be limited by an expression involving the Carnot efficiency and the mutual information gained in time t_M. Power output follows distinct scaling laws in short and long measurement time limits, and accounting for the energy cost of erasing the demon's memory sets a minimum time for the engine to produce positive work.

Core claim

We establish that the efficiency η of QSE is bounded by η≤1-(1-η_C)ln2/I(t_M), where I(t_M)/ln2 characterizes the ideality of quantum measurement, and approaches 1 for the Carnot efficiency reached under ideal measurement in quasi-static regime. We find that the power of QSE scales as P∝t_M^3 in the short-time regime and as P∝t_M^{-1} in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work.

What carries the argument

The mutual information I(t_M) captured by the Maxwell's demon during finite-time probing of the particle's spin state, which quantifies the which-way information and determines the efficiency bound.

If this is right

  • The efficiency bound reaches the Carnot limit when I(t_M) approaches ln 2 in the quasi-static regime.
  • Power increases proportionally to t_M cubed when measurement time is short.
  • Power decreases proportionally to 1/t_M when measurement time is long.
  • A threshold measurement time exists below which the engine cannot produce positive net work after memory erasure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Choosing an optimal finite t_M could balance efficiency and power for maximum performance.
  • The scaling behaviors suggest a sweet spot in operation time for practical information engines.
  • This bound may apply to other quantum engines where information extraction takes finite time.

Load-bearing premise

The model assumes that the mutual information I(t_M) obtained from finite-time spin-state probing by the demon can be directly inserted into the efficiency bound formula in the stated manner, and that Landauer's principle applies without modification to set the erasure cost threshold for net positive work.

What would settle it

Experimental verification of whether the measured efficiency of the engine stays below or reaches the derived bound for different values of t_M, and whether net positive work appears only after the predicted threshold time.

Figures

Figures reproduced from arXiv: 2303.14619 by C. P. Sun, Tan-Ji Zhou, Yu-Han Ma.

Figure 1
Figure 1. Figure 1: Schematic illustration of the Szilard engine cycle. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Measurement idealityM(t) = I(t)/ln2 with dif￾ferent α. The blue dashed curve, orange solid curve, and yellow dotted curve are plotted with α = 0.2, α = 0.4, and α = 2, respectively. (b) Efficiency and power of the engine as the function of dimensionalized measurement time, where ηC = 0.6, α = 0.4 are used. The grey solid curve and the black dotted curve mark P(t˜) and PO(t˜) respectively, which are nor… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Efficiency at maximum power of QSE as a [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Schematic illustration of Stern-Gerlach experiment. The inhomogeneous magnetic field along [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the spatial wave packet with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The width of the range of ηC that the efficiency at maximum power(EMP) can exceed η+ in two-dimensional parameter space (α, CE). Lighter area corresponds to wider range of ηC within which EMP can exceed the typical bound of EMP η+ = ηC/(2 − ηC) [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Power-efficiency trade-off relation of the information heat engine, where the finite-time effects of both the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
read the original abstract

We propose a finite-time quantum Szilard engine (QSE) with a quantum particle with spin as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time $t_{{\rm M}}$ to capture the which-way information of the particle, quantified by the mutual information $I(t_{\rm{M}})$ between WS and MD. We establish that the efficiency $\eta$ of QSE is bounded by $\eta\leq1-(1-\eta_{\rm{C}}){\rm ln}2/I(t_{{\rm M}})$, where $I(t_{{\rm M}})/\rm{ln}2$ characterizes the ideality of quantum measurement, and approaches $1$ for the Carnot efficiency reached under ideal measurement in quasi-static regime. We find that the power of QSE scales as $P\propto t_{{\rm M}}^{3}$ in the short-time regime and as $P\propto t_{\rm M}^{-1}$ in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript models a finite-time quantum Szilard engine with a spin-1/2 working substance and a Maxwell's demon that acquires mutual information I(t_M) via finite-time spin measurement. It claims an efficiency upper bound η ≤ 1 - (1 - η_C) ln2 / I(t_M) that recovers the Carnot limit for ideal quasi-static measurement, power scalings P ∝ t_M^3 (short-time) and P ∝ t_M^{-1} (long-time), and the existence of a threshold measurement time t_M^* beyond which net work is positive once the Landauer's erasure cost is subtracted.

Significance. If the derivations hold, the results supply explicit finite-time trade-offs for an information engine, with the efficiency bound directly incorporating measurement ideality through I(t_M) and the power scalings identifying distinct operating regimes; the threshold-time result further quantifies when information engines can overcome erasure overhead.

major comments (1)
  1. [section on net work / threshold time] The section deriving the threshold time t_M^* for positive net work: the efficiency bound replaces the ideal bit with the factor ln2/I(t_M), yet the erasure term is described only as 'the energy cost for erasing the MD's memory' without an explicit statement that the cost scales as kT I(t_M) rather than the full kT ln2. Using the unmodified kT ln2 would overestimate the cost whenever I(t_M) < ln2 and render the reported t_M^* inconsistent with the partial-information accounting already used in the efficiency bound.
minor comments (2)
  1. Notation for the measurement time is inconsistent between the abstract (t_M) and the displayed equations (t_{rm M}); standardize throughout.
  2. The abstract states the efficiency bound and power scalings but does not reference the equation numbers where they are derived; add cross-references for readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting a consistency issue in the treatment of the erasure cost relative to the mutual-information accounting used in the efficiency bound. We address the point directly below.

read point-by-point responses

  1. Referee: [section on net work / threshold time] The section deriving the threshold time t_M^* for positive net work: the efficiency bound replaces the ideal bit with the factor ln2/I(t_M), yet the erasure term is described only as 'the energy cost for erasing the MD's memory' without an explicit statement that the cost scales as kT I(t_M) rather than the full kT ln2. Using the unmodified kT ln2 would overestimate the cost whenever I(t_M) < ln2 and render the reported t_M^* inconsistent with the partial-information accounting already used in the efficiency bound.

    Authors: We agree that consistency requires the erasure cost to be scaled with the acquired mutual information. The efficiency bound already incorporates the finite-time ideality through the factor ln2/I(t_M). The minimal thermodynamic cost of erasure, consistent with the generalized Landauer principle for partial information, is therefore k_B T I(t_M) (with I(t_M) expressed in nats). The manuscript invokes Landauer's principle but does not explicitly write the scaling with I(t_M) or confirm that the threshold-time calculation employs this reduced cost. We will revise the relevant section (and the associated derivation of t_M^*) to state the erasure cost explicitly as k_B T I(t_M) and to recompute the threshold if the original numerical value was obtained with the unmodified k_B T ln2. This change preserves the physical content of the finite-time trade-off while removing the internal inconsistency. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives the efficiency bound η ≤ 1-(1-η_C)ln2/I(t_M) from mutual information I(t_M) obtained via finite-time spin probing, reports power scalings P∝t_M^3 (short-time) and P∝t_M^{-1} (long-time) from explicit time-regime analysis, and identifies a threshold time for net positive work after subtracting the Landauer's erasure cost. These steps invoke external principles (mutual information, Carnot limit, Landauer's principle) without any reduction of outputs to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations. The derivation chain remains self-contained and independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that Landauer's principle governs the memory-erasure energy cost and that mutual information I(t_M) for finite-time spin measurement is well-defined and directly usable in the efficiency inequality.

axioms (1)
  • domain assumption Landauer's principle applies to the energy cost of erasing the Maxwell's demon's memory
    Invoked to establish the existence of a threshold measurement time guaranteeing positive net work.

pith-pipeline@v0.9.0 · 5753 in / 1457 out tokens · 37154 ms · 2026-05-24T09:19:53.695727+00:00 · methodology

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Reference graph

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