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arxiv: 2604.10651 · v1 · submitted 2026-04-12 · 🪐 quant-ph

Role of Asymmetry in the Performance Optimization of a Relativistic Quantum Otto Engine

Monika , Shishram Rebari This is my paper

Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords relativistic quantum Otto engineasymmetrysudden compressionsudden expansionOmega functionefficiencywork optimizationphase diagram
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The pith

Asymmetry in a relativistic quantum Otto engine allows efficiency to approach unity in sudden compression but restricts it to one-half in sudden expansion.

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

The paper investigates the role of asymmetry in the two adiabatic legs of a relativistic quantum Otto engine powered by a time-dependent harmonic oscillator. It distinguishes sudden compression from sudden expansion scenarios and uses the Omega function to analytically find efficiency. The results show efficiency nearing 1 for sudden compression and capped at 1/2 for sudden expansion, with faster oscillator speeds increasing work and expanding the engine regime. This matters for understanding how timing and relativistic velocity can be tuned to improve quantum engine performance beyond symmetric cases.

Core claim

Imposing asymmetry on the adiabatic processes yields distinct sudden compression and sudden expansion scenarios in the relativistic quantum Otto cycle. The efficiency approaches unity in the sudden compression case, while it is restricted to one-half for the sudden expansion case. The Omega function unifies the characterization of efficiency and work, and increasing the oscillator velocity enhances work output, efficiency, and the size of the engine operational region.

What carries the argument

The Omega function as a unified performance metric that combines efficiency and extracted work for the asymmetric relativistic Otto engine.

If this is right

  • Efficiency approaches unity under sudden compression.
  • Efficiency is restricted to one-half under sudden expansion.
  • Increasing oscillator velocity enhances both the extracted work and efficiency.
  • The loop-shaped efficiency-work plots identify optimal operating points.
  • The operational region for the engine mode expands with increasing oscillator velocity while the refrigeration regime shrinks.

Where Pith is reading between the lines

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

  • This suggests that deliberate asymmetry can be used to prioritize high-efficiency operation in quantum heat engines.
  • Velocity tuning offers a control parameter to switch between engine and refrigerator modes in relativistic quantum systems.
  • Similar asymmetry effects may apply to other quantum thermodynamic cycles, potentially improving their performance.
  • Experimental realization could involve systems with controllable rapid frequency changes at relativistic speeds.

Load-bearing premise

The sudden approximation for the adiabatic legs remains valid in the relativistic regime.

What would settle it

A direct computation of the efficiency in the sudden compression case that yields a value significantly below unity when using full relativistic energy relations instead of the Omega function.

Figures

Figures reproduced from arXiv: 2604.10651 by Monika, Shishram Rebari.

Figure 1
Figure 1. Figure 1: FIG. 1: Diagrammatic illustration of a quantum Otto cycle based on a time-dependent harmonic oscillator. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Plot of the efficiency at the maximum Omega function with the Carnot efficiency for different values of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Variation of work output with the ratio of frequencies [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Parametric plots of work versus efficiency for the sudden compression (solid curves) and sudden expansion [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Phase diagram of an asymmetric relativistic Otto cycle plotted as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Phase diagram of asymmetric relativistic Otto cycle with sudden expansion stroke, plotted against [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

We present an analytical study of the relativistic quantum Otto cycle driven by a time-dependent harmonic oscillator. By imposing an asymmetry on the two adiabatic processes of this cycle, we obtain distinct scenarios of sudden compression and sudden expansion, and analyze how asymmetry affects the performance of the relativistic quantum Otto engine. By leveraging the Omega function as a unified performance metric, we analytically characterize the efficiency in both scenarios. Our findings demonstrate that the efficiency approaches unity in the sudden compression case, while it is restricted to one-half for the sudden expansion case. Furthermore, we investigate the impact of increasing oscillator velocity on the extracted work and identify parameter regimes where either sudden compression or sudden expansion dominates. Additionally, we examine the optimal operating point using parametric efficiency-work plots, whose loop-shaped structure shows that increasing oscillator velocity enhances both work output and efficiency. Finally, through a detailed phase diagram analysis of the Otto cycle, we observe that the operational region corresponding to the engine mode expands with increasing oscillator velocity, while the refrigeration regime shrinks correspondingly.

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 / 1 minor

Summary. The manuscript presents an analytical study of a relativistic quantum Otto cycle driven by a time-dependent harmonic oscillator, with asymmetry imposed on the two adiabatic legs to create distinct sudden-compression and sudden-expansion scenarios. Using the Omega function as a unified metric, it derives efficiency expressions showing that efficiency approaches unity in the sudden-compression case and is limited to one-half in the sudden-expansion case. The work further examines the dependence of extracted work on oscillator velocity, identifies optimal points via parametric efficiency-work plots that exhibit a loop-shaped structure, and analyzes phase diagrams in which the engine-mode region expands while the refrigeration regime shrinks as velocity increases.

Significance. If the central derivations hold, the results would be significant for relativistic quantum thermodynamics: they supply concrete, velocity-dependent efficiency bounds and phase diagrams for asymmetric Otto cycles, together with a clear visualization of efficiency-work trade-offs. The analytic treatment and the use of the Omega function to unify performance metrics constitute a strength, provided the underlying approximations are controlled.

major comments (1)
  1. [Efficiency derivation for sudden limits (abstract and main analytic sections)] The headline efficiency limits (approaching 1 for sudden compression, 1/2 for sudden expansion) are obtained by imposing the sudden limit on the adiabatic legs and inserting the resulting work and heat into the Omega function. This construction rests on two unverified steps that are load-bearing for the claims: (i) the sudden approximation remains valid when the oscillator velocity approaches c, and (ii) the standard non-relativistic expressions for internal energy, heat, and work continue to hold without Lorentz-frame corrections or additional relativistic contributions to the first law. Neither step is independently checked, so the reported limits inherit the same uncontrolled approximation flagged in the abstract.
minor comments (1)
  1. The abstract refers to 'parametric efficiency-work plots, whose loop-shaped structure' and to 'detailed phase diagram analysis' without citing specific figure numbers or describing the axes and parameter ranges; adding these references and a brief caption summary would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and for identifying the key assumptions underlying our efficiency derivations. We address the concern about the sudden-limit analysis point by point below. We maintain that the reported limits follow directly from the model's construction, but we agree that additional clarification on the reference frame and approximation regime will strengthen the manuscript.

read point-by-point responses

  1. Referee: [Efficiency derivation for sudden limits (abstract and main analytic sections)] The headline efficiency limits (approaching 1 for sudden compression, 1/2 for sudden expansion) are obtained by imposing the sudden limit on the adiabatic legs and inserting the resulting work and heat into the Omega function. This construction rests on two unverified steps that are load-bearing for the claims: (i) the sudden approximation remains valid when the oscillator velocity approaches c, and (ii) the standard non-relativistic expressions for internal energy, heat, and work continue to hold without Lorentz-frame corrections or additional relativistic contributions to the first law. Neither step is independently checked, so the reported limits inherit the same uncontrolled approximation flagged in the abstract.

    Authors: We appreciate the referee drawing attention to these foundational steps. In the manuscript the relativistic character of the engine is introduced solely through the velocity v of the time-dependent harmonic oscillator (the driving parameter), while the quantum system is described by the standard non-relativistic spectrum E_n = ħω(n + 1/2). The sudden limit is defined by the condition that the frequency-modulation time τ ≪ 2π/ω; this inequality is independent of v and remains valid even as v → c because it concerns the relative time scale between the external drive and the oscillator period in the instantaneous rest frame. Work and heat are computed from the change in occupation probabilities and the instantaneous energy eigenvalues after each sudden frequency jump; the first law is applied in that same instantaneous frame. Lorentz transformations affect only the laboratory-frame duration of the strokes and the extracted work through the relativistic factor appearing in the velocity-dependent expressions, but they do not alter the internal-energy differences used for the efficiency calculation. We therefore regard the analytic limits as controlled within the effective model employed. Nevertheless, we acknowledge that an explicit discussion of the reference-frame choice and the range of validity of the sudden approximation at relativistic speeds was not provided. We will add a short subsection (new Section II.C) that (a) states the instantaneous-rest-frame assumption, (b) shows that the sudden condition is frame-independent to leading order, and (c) notes the absence of additional relativistic corrections to the oscillator spectrum under the adopted effective description. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; analytic limits follow directly from model equations

full rationale

The paper applies the sudden limit to the two asymmetric adiabatic legs of the relativistic quantum Otto cycle, substitutes the resulting expressions for work and heat into the Omega function, and obtains the stated efficiency bounds (unity for sudden compression, one-half for sudden expansion) as direct mathematical consequences. No step reduces by definition to its own output, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests solely on a self-citation whose content is itself unverified within the present derivation. The Omega function is used as an external performance metric whose definition is independent of the specific efficiency limits being derived. The derivation chain therefore remains self-contained against the paper's own equations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the validity of the sudden approximation for the adiabatic strokes, the form of the relativistic time-dependent harmonic-oscillator Hamiltonian, and the definition of the Omega function as a performance metric. No new particles or forces are introduced.

free parameters (2)
  • asymmetry parameter between compression and expansion times
    Chosen to define the two distinct sudden scenarios; its value controls which efficiency limit is realized.
  • oscillator velocity
    Treated as a tunable parameter whose increase is shown to enlarge the engine regime.
axioms (2)
  • domain assumption The time-dependent harmonic oscillator Hamiltonian remains valid under relativistic boosts
    Invoked to justify the relativistic quantum Otto cycle.
  • domain assumption Sudden approximation applies to the adiabatic legs
    Required for the analytic efficiency expressions.

pith-pipeline@v0.9.0 · 5468 in / 1414 out tokens · 24940 ms · 2026-05-10T15:40:22.960842+00:00 · methodology

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Reference graph

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