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arxiv: 2412.13925 · v2 · pith:QCGVMBNUnew · submitted 2024-12-18 · ❄️ cond-mat.stat-mech · physics.class-ph

Revisiting Endo-reversible Carnot engine: Extending the Yvon engine

Xiu-Hua Zhao , Yu-Han Ma This is my paper

Pith reviewed 2026-05-23 07:16 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech physics.class-ph
keywords endo-reversible Carnot engineYvon engineCurzon-Ahlborn engineefficiency at maximum powerfinite-time thermodynamicssteady-statecyclic operation
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The pith

Extending the Yvon engine shows it is equivalent to the Curzon-Ahlborn engine as steady-state and cyclic forms of the endo-reversible Carnot heat engine.

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

The paper starts from the 1955 Yvon engine, which produced the same efficiency at maximum power as the later Curzon-Ahlborn engine but was limited by its special setup. The authors extend the Yvon model until it reaches the same level of generality as the CA engine. Rigorous comparison then shows the two are equivalent descriptions of the endo-reversible Carnot heat engine, one in steady-state form and the other in cyclic form. The extended Yvon derivation is presented as a simpler route into non-equilibrium thermodynamics for teaching.

Core claim

The extended Yvon engine and the CA engine represent the steady-state and cyclic forms of the endo-reversible Carnot heat engine respectively and are equivalent.

What carries the argument

The extension of the Yvon engine that removes its original special-setup limitations and permits direct equivalence proof with the CA engine.

Load-bearing premise

Extending the Yvon engine's special setup produces a model with exactly the same generality as the CA engine without adding hidden constraints.

What would settle it

A calculation of efficiency at maximum power for the extended Yvon engine that yields a different numerical result from the CA engine under matching conditions.

Figures

Figures reproduced from arXiv: 2412.13925 by Xiu-Hua Zhao, Yu-Han Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. Steady-state [(a) and (b)] and cyclic [(c) and (d)] endoreversible heat engines. (a) In the original Yvon engine, finite heat flux (denoted [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Trade-off relations between power and efficiency for the CA [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

A famous paper [Am. J. Phys. 43, 22 (1975)] unveiled the efficiency at maximum power (EMP) of the endo-reversible Carnot heat engine, now commonly referred to as the Curzon-Ahlborn (CA) engine, pioneering finite-time thermodynamics. Historically, despite the significance of the CA engine, similar findings had emerged at an earlier time, such as the Yvon engine proposed by J. Yvon in 1955 sharing the exact same EMP. However, the special setup of the Yvon engine has circumscribed its broader influence. This paper extends the Yvon engine model to achieve a level of generality comparable to that of the CA engine. A rigorous comparison reveals that the extended Yvon engine and CA engine represent the steady-state and cyclic forms of the endo-reversible Carnot heat engine, respectively, and are equivalent. Our work provides a pedagogical example for the teaching of thermodynamics and engineering thermodynamics, given that the simple and lucid derivation of the extended Yvon engine helps students initiate their understanding of non-equilibrium thermodynamics.

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

0 major / 2 minor

Summary. The manuscript extends the 1955 Yvon engine to a more general form comparable to the Curzon-Ahlborn (CA) engine. It claims that the extended Yvon model (steady-state) and the CA model (cyclic) are equivalent representations of the endo-reversible Carnot heat engine under identical linear heat-transfer laws, both recovering the same algebraic expression for efficiency at maximum power (EMP). The work presents an explicit, parameter-free derivation of the extended Yvon engine followed by side-by-side comparison, positioning the result as a pedagogical example for finite-time thermodynamics.

Significance. If the equivalence holds, the paper supplies a clear, simple derivation that can serve as an entry point for students learning non-equilibrium thermodynamics. The explicit parameter-free derivation and direct comparison of EMP expressions are strengths. The stress-test concern about hidden constraints from the extension does not appear to land, as the mapping preserves generality without additional restrictions on timing or coupling.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'rigorous comparison' would be more accessible if it briefly indicated the main steps (e.g., the form of the extended heat-transfer law or the EMP derivation) rather than leaving the reader to infer them from the full text.
  2. [Introduction] The introduction would benefit from an explicit citation to the original 1955 Yvon reference when first describing the special setup, to strengthen the historical framing.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation for minor revision. The report highlights the pedagogical value of the explicit derivation and the equivalence between the extended Yvon engine and the Curzon-Ahlborn engine. No specific major comments were listed under the MAJOR COMMENTS section.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation begins from the 1955 Yvon setup, performs an explicit algebraic extension to match the generality of the 1975 CA model, and then compares the resulting EMP expressions side-by-side. Both the extension and the equivalence proof are parameter-free, use only the stated linear heat-transfer law, and do not invoke self-citations or fitted inputs for the central claim. The cited historical works are external and predate the present authors. No step reduces by construction to its own inputs; the argument remains self-contained against the external benchmarks of the two classic models.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work rests on the standard domain assumption of endo-reversibility in finite-time thermodynamics; no new free parameters, ad-hoc axioms, or invented entities are introduced.

axioms (1)
  • domain assumption Endo-reversible Carnot engine assumes internal processes are reversible while external heat transfers occur in finite time.
    This is the foundational model being revisited and extended.

pith-pipeline@v0.9.0 · 5719 in / 1152 out tokens · 32281 ms · 2026-05-23T07:16:11.921241+00:00 · methodology

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Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 1 internal anchor

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