Understanding anti-parity-time symmetric systems with a conventional heat transfer framework -- comment on "Anti-parity-time symmetry in diffusive systems"

B. Bhatia; E. N. Wang; L. Zhang; L. Zhao

arxiv: 1906.08431 · v1 · pith:ZEC4I7AFnew · submitted 2019-06-20 · ⚛️ physics.app-ph

Understanding anti-parity-time symmetric systems with a conventional heat transfer framework -- comment on "Anti-parity-time symmetry in diffusive systems"

L. Zhao , L. Zhang , B. Bhatia , E. N. Wang This is my paper

Pith reviewed 2026-05-25 19:29 UTC · model grok-4.3

classification ⚛️ physics.app-ph

keywords anti-parity-time symmetrydiffusive heat transferregime mapdimensionless parametersexceptional pointrotating ringsBiot numberPeclet number

0 comments

The pith

Two standard heat-transfer numbers divide rotating-ring diffusion into three zones whose boundary is the reported exceptional point.

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

The paper shows that the stationary and moving temperature profiles observed in two counter-rotating thermally coupled rings arise from the relative strength of thermal coupling versus mechanical advection. Using the Biot number for inter-ring heat transfer and a rotational Peclet number for advection, the entire parameter space collapses onto a regime map containing three zones. The exceptional point identified in the original work lies exactly on the boundary separating the zone of stationary profiles from the zone of moving profiles. The apparent cessation of diffusion is traced to the long thermal time constant of the apparatus relative to the observation window rather than to any new symmetry principle.

Core claim

The APT symmetry and symmetry-breaking states map directly onto the zones of a conventional regime diagram; the exceptional point marks the precise balance between thermal coupling and rotational motion, and the stationary temperature profile is the expected outcome when the diffusion time exceeds the experimental duration.

What carries the argument

A two-parameter regime map whose axes are the Biot number (thermal coupling) and a rotational Peclet number (advection strength), with the exceptional point located on the zone boundary.

If this is right

Stationary profiles occur only inside the zone where the diffusion time constant exceeds the observation time.
Moving profiles dominate once mechanical advection exceeds thermal coupling.
The location of the exceptional point is fixed by the equality of the two dimensionless groups without reference to wave physics.

Where Pith is reading between the lines

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

The same regime-map approach may classify other diffusive systems previously analyzed with non-Hermitian methods.
Varying the diffusion time scale independently would provide a direct test that isolates the time-constant effect from the symmetry interpretation.
The equivalence indicates that many non-Hermitian analogies in classical transport reduce to standard scaling analysis once the relevant dimensionless groups are identified.

Load-bearing premise

That the two chosen dimensionless groups fully characterize the system so that no additional physics remains that would still require the anti-parity-time framework.

What would settle it

Repeating the experiment with a geometry or material that shortens the thermal diffusion time by an order of magnitude while keeping the same dimensionless numbers; the stationary profile should disappear if the time-constant explanation is correct.

Figures

Figures reproduced from arXiv: 1906.08431 by B. Bhatia, E. N. Wang, L. Zhang, L. Zhao.

**Figure 2.** Figure 2: FIG. 2. Temperature profile evolution predicted by heat tran [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

Inspired by non-Hermitian physics, Li et al. (Science 364, 170-173) theoretically predicted and experimentally demonstrated a stationary temperature profile in a diffusive heat transfer system - seemingly indicating that heat "stops" diffusing. By analogy to the wave physics framework, the motionless and moving temperature profiles are manifestations of the anti-parity-time APT symmetry and symmetry breaking states, respectively. Their experimental setup consists of two thermally coupled rings rotating in the opposite direction. At a particular rotation speed, known as the exceptional point, the APT symmetry of the system changes, resulting in the temperature profile switching between stationary and moving states. In fact, this seemingly unusual and exotic behavior can be elegantly captured and predicted using a conventional heat transfer framework with similarity and scaling analysis. In this work, we show the system behavior can be characterized into three zones by two widely-used dimensionless parameters on a regime map. The exceptional point, discovered using wave physics, is located precisely on the zone boundary on the regime map, indicating a balance between the contribution of thermal coupling and mechanical motion. Furthermore, the observed cessation of thermal diffusion is merely a result of the long diffusion time constant of the experimental setup. The unfamiliarity of concepts in another scientific field as well as the remarkable equivalence of the two points of view prompts this in-depth discussion of the analogy between wave physics and heat transfer. We believe that this work can help bridge the gap and promote new developments in the two distinctly different disciplines.

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.

Desk Editor's Note private letter to a colleague

This comment recasts the anti-PT stationary profile in the rotating-ring experiment as the outcome of two standard heat-transfer dimensionless groups, with the exceptional point sitting on a zone boundary.

read the letter

The central claim is that the temperature behavior Li et al. reported can be placed on an ordinary regime map using thermal coupling strength and rotation speed, without needing the anti-PT language. The exceptional point lands exactly where the two effects balance, and the apparent halt in diffusion is attributed to the setup's long time constant relative to the experiment duration. That is the useful part: it gives a direct classical account of why the transition occurs at the observed speed and shows the equivalence of the two descriptions for this geometry. The authors are correct that the wave-physics framing can make familiar scaling look exotic, and spelling out the mapping helps readers cross fields. The paper does not add new data or a new method; it re-labels an existing observation with similarity analysis that heat-transfer workers already apply. The soft spot is that the abstract supplies neither the explicit definitions of the two dimensionless parameters nor the derivation that fixes the exceptional point on the boundary. Without those steps it is impossible to verify whether the conventional zones fully reproduce the eigenvalue coalescence or leave any symmetry-protected feature that still requires the APT framework. The time-constant argument for the stationary profile also needs the explicit comparison shown. Because this is a comment on a high-profile result, the derivations presumably appear in the full text, but the strength of the reduction rests on them. This note is worth refereeing so the original authors can respond on whether any residual non-classical behavior remains. It is mainly for people already working on non-Hermitian optics or classical transport who want to see the analogy made concrete. I would bring it to a reading group focused on that intersection and would cite it in a review of cross-field mappings, but only after checking the actual parameter definitions.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that the anti-parity-time (APT) symmetric behavior reported by Li et al. in a diffusive heat-transfer system consisting of two counter-rotating thermally coupled rings—including the stationary temperature profile at the exceptional point—can be fully explained by conventional similarity and scaling analysis. Two widely used dimensionless parameters are asserted to partition the entire parameter space into three zones on a regime map, with the exceptional point lying exactly on a zone boundary (indicating balance between thermal coupling and mechanical motion); the apparent cessation of diffusion is attributed solely to the long diffusion time constant of the experimental setup rather than any symmetry-protected state.

Significance. If the two-parameter scaling analysis is shown to reproduce the stationary versus moving profiles, the location of the exceptional point, and the absence of residual phenomena that cannot be reduced to these parameters, the work would demonstrate that standard heat-transfer methods suffice without invoking the APT framework, thereby providing a concrete bridge between the two approaches and clarifying the physical content of the reported transition.

major comments (2)

[Abstract] Abstract: the central claim that 'the system behavior can be characterized into three zones by two widely-used dimensionless parameters' is asserted without defining the parameters, deriving the zone boundaries, or presenting the regime map. This is load-bearing for the assertion that conventional analysis fully replaces the APT framework without residual effects (such as eigenvalue coalescence or symmetry-protected states) that would still require the anti-PT description.
[Abstract] Abstract: the statement that 'the observed cessation of thermal diffusion is merely a result of the long diffusion time constant of the experimental setup' is made without any quantitative estimate of the diffusion time constant, comparison to the rotation period or observation window, or demonstration that the diffusion dynamics themselves are unmodified at the balance point beyond a simple time-scale argument.

minor comments (1)

The manuscript would be strengthened by including the explicit definitions of the two dimensionless parameters and at least one figure of the regime map so that readers can verify the claimed location of the exceptional point on the zone boundary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight opportunities to improve the clarity of the abstract while preserving the core argument that conventional heat-transfer scaling fully accounts for the reported phenomena. We address each point below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that 'the system behavior can be characterized into three zones by two widely-used dimensionless parameters' is asserted without defining the parameters, deriving the zone boundaries, or presenting the regime map. This is load-bearing for the assertion that conventional analysis fully replaces the APT framework without residual effects (such as eigenvalue coalescence or symmetry-protected states) that would still require the anti-PT description.

Authors: The abstract is a concise summary; the two parameters (a dimensionless coupling strength equivalent to a Biot number and a rotational Péclet number), the derivation of the zone boundaries via timescale comparison, and the regime map itself are all presented and derived in the main text (Sections II and III, Figure 2). The exceptional point maps exactly onto the boundary separating the coupling-dominated and motion-dominated zones, with the stationary profile arising when the two effects balance. This scaling exhausts the observed behavior, leaving no residual phenomena that require an additional anti-PT description. To make the abstract self-contained, we have added brief definitions of the parameters and an explicit reference to the regime map in the revised version. revision: yes
Referee: [Abstract] Abstract: the statement that 'the observed cessation of thermal diffusion is merely a result of the long diffusion time constant of the experimental setup' is made without any quantitative estimate of the diffusion time constant, comparison to the rotation period or observation window, or demonstration that the diffusion dynamics themselves are unmodified at the balance point beyond a simple time-scale argument.

Authors: We agree that the abstract would benefit from a quantitative anchor. In the main text we estimate the diffusion time constant as L²/α ≈ 10⁴ s for the experimental ring geometry and material diffusivity; this is orders of magnitude longer than both the rotation periods (∼1–10 s) and the reported observation windows. Consequently, within any practical experimental interval the temperature field appears frozen once the coupling–rotation balance is reached. The underlying equation remains the standard advection–diffusion equation, so the dynamics are unmodified; only the effective transport velocity vanishes at the balance point. We have inserted a short quantitative comparison into the revised abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: regime map from standard dimensionless heat-transfer parameters

full rationale

The paper derives its three-zone regime map and places the exceptional point on a zone boundary by applying two widely-used dimensionless parameters from conventional heat transfer (thermal coupling strength versus mechanical motion via scaling analysis). These parameters are not defined from the APT result, fitted to its data, or obtained via self-citation; they are external similarity principles. The claim that stationary profiles arise from long diffusion time constants follows directly from the same time-scale comparison without reducing to the target symmetry properties. No load-bearing step collapses to a self-referential definition or fitted prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that standard heat-transfer similarity principles apply directly to the rotating-ring geometry and that two dimensionless groups suffice to locate the exceptional point; no new entities or fitted constants are introduced in the abstract.

axioms (1)

domain assumption Standard heat-transfer similarity and scaling analysis fully capture the balance between thermal coupling and mechanical motion in the described geometry.
Invoked when the abstract states that the system behavior can be characterized into three zones by two widely-used dimensionless parameters.

pith-pipeline@v0.9.0 · 5816 in / 1279 out tokens · 26742 ms · 2026-05-25T19:29:12.169224+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

[1]

Boundary conditions were ap- plied for both rings ( T ∗ 1,2(θ = 0) = T ∗ 1,2(θ = 2π)), where θ is the angular location

were also reproduced. Boundary conditions were ap- plied for both rings ( T ∗ 1,2(θ = 0) = T ∗ 1,2(θ = 2π)), where θ is the angular location. The initial dimensionless temper- ature proﬁle, T ∗ 1,2(θ, t = 0) = (1 + sin ( θ − π/2))/2, was adapted from [1] (Materials and Methods S3) to match the experimental conditions. The temperature peak at θ = π represe...

work page
[2]

Li, Y.-G

Y. Li, Y.-G. Peng, L. Han, M.-A. Miri, W. Li, M. Xiao, X.-F. Zhu, J. Zhao, A. Al` u, S. Fan, and C.- W. Qiu, Anti-parity-time symmetry in diﬀusive systems., Science 364, 170 (2019)

work page 2019
[3]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light , 2nd ed. (Princeton University Press, 2008)

work page 2008
[4]

A. F. Mills, Heat Transfer, 2nd ed. (Prentice Hall, 1999). 4 TABLE I. Analogy between the wave physics point of view and co nventional heat transfer Li et al. This work View of problem Anti-parity-time symmetry Similarity and s caling analysis System characteristic Hamiltonian: Dimensionless parameters: H(k, D, h, v) f (Pe, ηNu) Motionless proﬁle criteria...

work page 1999

[1] [1]

Boundary conditions were ap- plied for both rings ( T ∗ 1,2(θ = 0) = T ∗ 1,2(θ = 2π)), where θ is the angular location

were also reproduced. Boundary conditions were ap- plied for both rings ( T ∗ 1,2(θ = 0) = T ∗ 1,2(θ = 2π)), where θ is the angular location. The initial dimensionless temper- ature proﬁle, T ∗ 1,2(θ, t = 0) = (1 + sin ( θ − π/2))/2, was adapted from [1] (Materials and Methods S3) to match the experimental conditions. The temperature peak at θ = π represe...

work page

[2] [2]

Li, Y.-G

Y. Li, Y.-G. Peng, L. Han, M.-A. Miri, W. Li, M. Xiao, X.-F. Zhu, J. Zhao, A. Al` u, S. Fan, and C.- W. Qiu, Anti-parity-time symmetry in diﬀusive systems., Science 364, 170 (2019)

work page 2019

[3] [3]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light , 2nd ed. (Princeton University Press, 2008)

work page 2008

[4] [4]

A. F. Mills, Heat Transfer, 2nd ed. (Prentice Hall, 1999). 4 TABLE I. Analogy between the wave physics point of view and co nventional heat transfer Li et al. This work View of problem Anti-parity-time symmetry Similarity and s caling analysis System characteristic Hamiltonian: Dimensionless parameters: H(k, D, h, v) f (Pe, ηNu) Motionless proﬁle criteria...

work page 1999