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arxiv: 2604.07099 · v1 · submitted 2026-04-08 · ❄️ cond-mat.stat-mech

Balancing Power, Efficiency, and Constancy under Broken Time-Reversal Symmetry

Ousi Pan , Zhiqiang Fan , Shunjie Zhang , Liwei Chen , Jincan Chen , Shanhe Su This is my paper

Pith reviewed 2026-05-10 17:35 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords thermoelectric systemslinear responsetime-reversal symmetrypower-efficiency trade-offfluctuationsheat enginesnonequilibrium thermodynamicsconstancy
0
0 comments X

The pith

Trade-off bounds on power, efficiency and fluctuations remain valid for thermoelectric systems even when time-reversal symmetry is broken.

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

The paper derives general trade-off relations among power, efficiency and constancy for two-terminal thermoelectric systems in the linear response regime. Constancy is quantified by fluctuations of the output. These bounds continue to hold when time-reversal symmetry is broken, showing how the breaking modifies the constraints on steady-state energy conversion. A sympathetic reader would care because the relations indicate that broken-symmetry engines can reach near-Carnot efficiency while keeping finite power and controlled fluctuations, thereby outperforming conventional symmetric devices.

Core claim

We derive general trade-off relations among the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear response regime. The bounds of the efficiency, power and fluctuations are valid even when time-reversal symmetry is broken, revealing how such a symmetry breaking alters the fundamental constraints on steady-state energy conversion. Guided by this bound, heat engines with broken time-reversal symmetry can be operated at near-Carnot efficiency while maintaining finite power output and fluctuations, enabling them to outperform their traditional counterparts.

What carries the argument

General trade-off relations among power, efficiency and constancy derived from linear-response transport coefficients in two-terminal systems.

If this is right

  • The efficiency-power-constancy bounds apply even when time-reversal symmetry is broken.
  • Symmetry breaking changes the fundamental constraints on steady-state energy conversion.
  • Broken-symmetry heat engines can reach near-Carnot efficiency at finite power with controlled fluctuations.
  • The relations extend and refine earlier universal trade-off results in nonequilibrium thermodynamics.

Where Pith is reading between the lines

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

  • The same linear-response bounds could be tested in mesoscopic or quantum-dot thermoelectric devices where time-reversal symmetry is broken by magnetic fields.
  • If the bounds survive beyond linear response they would constrain design choices for active or driven energy converters.
  • Intentional breaking of time-reversal symmetry might be engineered in materials to loosen the usual power-efficiency limits.

Load-bearing premise

The derivation assumes the linear response regime for two-terminal thermoelectric systems, where currents are linearly related to thermodynamic forces.

What would settle it

An experimental measurement in a linear-response two-terminal thermoelectric device showing a violation of the derived power-efficiency-constancy bound when time-reversal symmetry is broken would falsify the relations.

Figures

Figures reproduced from arXiv: 2604.07099 by Jincan Chen, Liwei Chen, Ousi Pan, Shanhe Su, Shunjie Zhang, Zhiqiang Fan.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
read the original abstract

We derive general trade-off relations among the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear response regime. Constancy, which quantifies the steadiness of the heat engine, is measured by its fluctuations. The bounds of the efficiency, power and fluctuations are valid even when time-reversal symmetry is broken, revealing how such a symmetry breaking alters the fundamental constraints on steady-state energy conversion. Our results extend and refine previously established universal trade-offs, offering deeper insight into the performance limits in nonequilibrium thermodynamics. Guided by this bound, heat engines with broken time-reversal symmetry can be operated at near-Carnot efficiency while maintaining finite power output and fluctuations, enabling them to outperform their traditional counterparts.

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

2 major / 2 minor

Summary. The manuscript derives general trade-off relations among power, efficiency, and constancy (quantified via fluctuations) for two-terminal thermoelectric systems operating in the linear response regime. The central result is that these bounds remain valid when time-reversal symmetry is broken, by properly incorporating the antisymmetric component of the Onsager matrix while respecting the second-law constraint on entropy production. The work extends prior universal trade-offs and indicates that broken-TR S engines can be operated near Carnot efficiency with finite power output and controlled fluctuations, potentially outperforming symmetric counterparts.

Significance. If the derivations are rigorous, the result is significant because it refines the known efficiency-power-fluctuation trade-offs in nonequilibrium thermodynamics to include systems with broken time-reversal symmetry, a feature relevant to many experimental setups (e.g., those with magnetic fields). The explicit accounting for the antisymmetric Onsager terms provides a concrete handle on how symmetry breaking alters performance limits, which could inform the design and operation of thermoelectric devices.

major comments (2)
  1. [§3] §3, Eq. (12): the trade-off bound must be shown to reduce exactly to the known symmetric-TR S result when the antisymmetric coefficient vanishes; otherwise the claim of a consistent extension is not fully substantiated.
  2. [§4.2] §4.2: the statement that broken-TR S engines 'outperform' symmetric ones requires a direct, quantitative comparison (e.g., the allowed region in the power-efficiency plane for nonzero versus zero antisymmetric component) rather than a qualitative assertion.
minor comments (2)
  1. [Introduction] The definition of 'constancy' via fluctuations is introduced in the abstract but should be restated with a short equation or reference to prior literature in the introduction for readers unfamiliar with the term.
  2. [Throughout] Notation for the Onsager matrix elements (L_{ij}) and the asymmetry parameter should be made uniform across the text and figures to avoid ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments on our manuscript. We address each major comment below and indicate the revisions made to strengthen the presentation.

read point-by-point responses

  1. Referee: [§3] §3, Eq. (12): the trade-off bound must be shown to reduce exactly to the known symmetric-TR S result when the antisymmetric coefficient vanishes; otherwise the claim of a consistent extension is not fully substantiated.

    Authors: We agree that an explicit reduction to the time-reversal symmetric case is necessary to substantiate the extension. In the revised manuscript we have added, immediately after Eq. (12) in §3, a short derivation showing that the general bound reduces exactly to the known symmetric result upon setting the antisymmetric Onsager coefficient to zero. This recovers the previously established inequality and confirms consistency with the literature. revision: yes

  2. Referee: [§4.2] §4.2: the statement that broken-TR S engines 'outperform' symmetric ones requires a direct, quantitative comparison (e.g., the allowed region in the power-efficiency plane for nonzero versus zero antisymmetric component) rather than a qualitative assertion.

    Authors: The referee correctly notes that a quantitative comparison would strengthen the claim. We have revised §4.2 to include an explicit comparison of the allowed regions in the power-efficiency plane. Specifically, we derive the boundary of the feasible region as a function of the antisymmetric component and illustrate, via both analytic expressions and a numerical example under fixed entropy-production constraints, that a nonzero antisymmetric term can enlarge the operating region relative to the symmetric case, thereby supporting the potential for improved performance. revision: yes

Circularity Check

0 steps flagged

No circularity: bounds derived from linear-response Onsager relations with broken TRS

full rationale

The paper derives trade-off bounds on power, efficiency, and fluctuations directly from the linear-response framework for two-terminal systems, explicitly incorporating the antisymmetric part of the Onsager matrix to account for broken time-reversal symmetry while preserving entropy-production constraints. No step reduces a claimed prediction to a fitted parameter, self-definition, or load-bearing self-citation; the relations are obtained from the standard linear current-force equations and second-law inequalities without renaming known results or smuggling ansatzes. The central claim therefore remains self-contained against external benchmarks and does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on standard assumptions of linear irreversible thermodynamics; no free parameters, invented entities, or ad-hoc axioms are explicitly introduced in the provided text.

axioms (2)
  • domain assumption Linear response regime applies to two-terminal thermoelectric transport
    Explicitly stated in the abstract as the regime of the derivation.
  • domain assumption Fluctuations quantify constancy of the heat engine
    Defined in the abstract as the measure of steadiness.

pith-pipeline@v0.9.0 · 5431 in / 1114 out tokens · 70965 ms · 2026-05-10T17:35:58.174205+00:00 · methodology

discussion (0)

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Reference graph

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