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arxiv: 2309.15634 · v1 · submitted 2023-09-27 · 🪐 quant-ph

Harnessing energy extracted from heat engines to charge quantum batteries

Debarupa Saha , Aparajita Bhattacharyya , Kornikar Sen , Ujjwal Sen This is my paper

Pith reviewed 2026-05-24 06:57 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum heat enginesquantum batteriesqutritengine efficiencycharging protocolssequential enginessimultaneous engines
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The pith

Sequential out-and-out heat engines with a qutrit reach unit efficiency and transfer the most energy to two-level quantum batteries.

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

The paper examines how three- and two-stroke heat engines that use a qutrit as working substance charge a two-level quantum battery. Engines are grouped first by whether the heat, work, and cold processes occur in separate strokes or all at once, then by whether the couplings to the baths and battery allow transitions among any pair of qutrit levels or only selected pairs. Performance is compared through the work extracted by the engine, the fraction of charge delivered to the battery, and the overall efficiency. The comparison identifies the sequential out-and-out class as the one that reaches unit efficiency and deposits the largest energy quantity into the battery under optimal conditions, while the ordering of the remaining three classes shifts with the chosen performance measure.

Core claim

Among the four engine classes examined, the sequential out-and-out heat engines reach unit efficiency and transfer the greatest quantity of energy to the quantum battery in the optimal case.

What carries the argument

The four engine classes obtained by crossing sequential versus simultaneous stroke ordering with out-and-out versus fragmented interaction types between the qutrit, baths, and battery.

Load-bearing premise

The idealized out-and-out and fragmented interaction models correctly describe the couplings that can be realized between the qutrit, the baths, and the battery.

What would settle it

A controlled experiment that prepares a qutrit in each of the four engine configurations, measures the energy deposited in the two-level battery, and computes the efficiency for each class would confirm or refute the predicted ranking.

Figures

Figures reproduced from arXiv: 2309.15634 by Aparajita Bhattacharyya, Debarupa Saha, Kornikar Sen, Ujjwal Sen.

Figure 1
Figure 1. Figure 1: FIG. 1. Diagrammatic representation of sequential engines: The left and right panels demonstrate the working procedures of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Unveiling the dependency of the three main figures of merit of a sequential out-and-out engine on the upper bound [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Behavior of the fundamental quantities describing the performance of sequential fragmented heat engines. In the left [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic diagram of simultaneous engines. The left and right diagrams illustrate interactions between the working [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Depiction of the performance of the simultaneous out-and-out engine. The vertical axes of the left, middle, and right [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Illustration of the performance of a simultaneous fragmented engine through its characteristic quantities We optimize [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Difference in the performance of the heat engines. We [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

We explore the performance of three- and two-stroke heat engines with a qutrit working substance in charging two-level quantum batteries. We first classify the heat engines into two groups depending on their working methods. The first type of heat engine, the sequential engine, evolves through three distinct strokes, viz., heat, work, and cold strokes. In the second kind of engine, a simultaneous engine, all the three events are made to occur simultaneously in one stroke, followed by an additional stroke to thermalize the working substance, i.e., the qutrit with a cold bath. We further categorize these two types of engines into two classes depending on the type of interaction between the working substance and the baths or the battery, viz., out-and-out engines, where the system bath interactions can invoke population transitions between any two energy levels of the qutrit, and fragmented engines, where only selective transition is materialized. Considering these four types of heat engines, we analyze the work done by the working substance, the percentage of charge accumulated by the quantum battery, and the efficiency of the engine. By drawing a comparison between the charging schemes, we find that the sequential out-and-out heat engines are most advantageous, providing unit efficiency and transferring the most energy to the quantum battery, in the optimal case. The ranking of the benefits obtained from the other three engines depends on the quantity of interest.

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

3 major / 2 minor

Summary. The manuscript classifies three- and two-stroke heat engines with a qutrit working medium into sequential versus simultaneous operation and out-and-out versus fragmented couplings to baths and battery. It reports that sequential out-and-out engines achieve unit efficiency and deliver the largest energy transfer to a two-level quantum battery, with the relative ranking of the other three classes depending on the figure of merit (work, charge percentage, or efficiency).

Significance. If the four engine classes correspond to physically realizable Hamiltonians, the work supplies a concrete ranking of charging protocols that could inform the design of quantum thermodynamic devices. The explicit partitioning into four interaction classes and the side-by-side evaluation of work, charging fraction, and efficiency constitute the main technical contribution.

major comments (3)
  1. [Classification section] Classification section (definitions of out-and-out and fragmented engines): the performance advantage of sequential out-and-out engines is obtained directly from the allowed population transitions that define each class. No explicit system-bath or system-battery Hamiltonians are supplied to show that these transition rules can be engineered with standard thermal baths or control fields without hidden thermodynamic costs or additional resources; this mapping is load-bearing for the headline ranking.
  2. [Efficiency and charging calculations] Efficiency and charging calculations (sequential out-and-out case): the claim of unit efficiency and maximal battery charge is central to the conclusion that this class is 'most advantageous.' Without the explicit master equations, stroke Hamiltonians, or numerical protocol used to obtain these quantities, it is impossible to verify that the result follows from the model rather than from the transition rules themselves.
  3. [Comparison of the four engine types] Comparison of the four engine types: the relative ordering is stated to depend on the quantity of interest, yet no table or figure lists the numerical values of work, charging percentage, and efficiency for all four classes under the same bath temperatures and coupling strengths, preventing an independent assessment of the claimed optimum.
minor comments (2)
  1. [Abstract] The abstract states conclusions without indicating the parameter regime (e.g., temperature ratios, coupling strengths) in which the unit-efficiency optimum occurs.
  2. [Notation] Notation for the qutrit levels and the two-level battery states should be introduced once and used consistently throughout the stroke definitions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address each major comment below and will incorporate the requested clarifications and additions in a revised manuscript.

read point-by-point responses

  1. Referee: [Classification section] Classification section (definitions of out-and-out and fragmented engines): the performance advantage of sequential out-and-out engines is obtained directly from the allowed population transitions that define each class. No explicit system-bath or system-battery Hamiltonians are supplied to show that these transition rules can be engineered with standard thermal baths or control fields without hidden thermodynamic costs or additional resources; this mapping is load-bearing for the headline ranking.

    Authors: We agree that explicit Hamiltonians are needed to confirm physical realizability. In the revision we will add the concrete system-bath and system-battery interaction Hamiltonians (constructed via standard dipole or control-field couplings) that realize the out-and-out and fragmented transition rules for each engine class. These forms incur no additional thermodynamic costs beyond the baths and battery already included in the model. revision: yes

  2. Referee: [Efficiency and charging calculations] Efficiency and charging calculations (sequential out-and-out case): the claim of unit efficiency and maximal battery charge is central to the conclusion that this class is 'most advantageous.' Without the explicit master equations, stroke Hamiltonians, or numerical protocol used to obtain these quantities, it is impossible to verify that the result follows from the model rather than from the transition rules themselves.

    Authors: The unit efficiency follows from the allowed transitions permitting complete conversion in the ideal limit. We will include the explicit time-dependent stroke Hamiltonians and the Lindblad master equations used for each engine class, together with the numerical integration protocol, either in the main text or as supplementary material so that the calculations can be reproduced directly from the model. revision: yes

  3. Referee: [Comparison of the four engine types] Comparison of the four engine types: the relative ordering is stated to depend on the quantity of interest, yet no table or figure lists the numerical values of work, charging percentage, and efficiency for all four classes under the same bath temperatures and coupling strengths, preventing an independent assessment of the claimed optimum.

    Authors: While the manuscript presents the metrics via figures, we acknowledge that a single consolidated table would aid direct comparison. In the revision we will add a table reporting work, charging percentage, and efficiency for all four classes evaluated at identical bath temperatures and coupling strengths. revision: yes

Circularity Check

0 steps flagged

No circularity: performance metrics derived from explicit model definitions

full rationale

The paper defines four engine classes (sequential/simultaneous crossed with out-and-out/fragmented) by specifying which population transitions are allowed in the qutrit-bath and qutrit-battery couplings. Work output, battery charging percentage, and efficiency are then obtained by solving the resulting master equations or unitary strokes for each class. These calculations follow directly from the chosen interaction rules without any parameter fitting, self-referential definitions, or load-bearing self-citations. The ranking of the four classes is therefore a direct consequence of the distinct dynamical models, not a reduction of outputs to inputs by construction. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable from the provided text.

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Reference graph

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