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Theory of supercooled water

T0 review · 1 major / 1 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read A model of supercooled water links its liquid-liquid critical point to inversion thermodynamics of gas throttling.

desk verdict New model reproduces the Speedy-Angell and Poole pictures but the claimed analogy to Joule-Thomson inversion and black holes supplies no shown structural link that would add independent plausibility to the LLCP. read the letter →

arxiv 2605.24105 v1 pith:VI642PJG submitted 2026-05-22 cond-mat.stat-mech

Jacobo Troncoso , Claudio A. Cerdeiriña This is my paper · ORCID
classification cond-mat.stat-mech
keywords supercooledwaterliquid-liquidcriticalpointJoule-Thomsoninversionmetastableliquidsthermodynamicanalogystabilitylimit
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces a thermodynamic model for water that includes true supercooled liquid states metastable with respect to ice. Numerical solutions of the model recover both the stability-limit picture of Speedy and Angell and the metastable liquid-liquid critical point picture of Poole and colleagues. The authors identify an unnoticed analogy between the liquid-liquid critical point and the inversion curve in the Joule-Thomson throttling process for gases, with an extension to equivalent black hole phenomenology. This analogy is presented as lending significant theoretical plausibility to the actual existence of the liquid-liquid critical point in water.

What carries the argument

The analogy between water's liquid-liquid critical point and the inversion curve of the Joule-Thomson gas throttling process, which maps thermodynamic inversion behavior across systems.

What would settle it

A calculation or measurement showing that thermodynamic properties near any liquid-liquid critical point in supercooled water fail to match the inversion curve signatures of the Joule-Thomson process would remove the analogy's support for the critical point's existence.

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Extended reading notes

Core claim

Numerical solutions of a model contemplating metastable supercooled-liquid states reproduce the Speedy-Angell stability-limit picture and Poole et al.'s liquid-liquid criticality, with the real existence of the liquid-liquid critical point gaining significant theoretical plausibility from a hitherto unnoticed analogy with the inversion thermodynamics of the Joule-Thomson gas throttling process and equivalent black hole phenomenology.

Load-bearing premise

The model assumes true supercooled-liquid states that are metastable with respect to crystalline solids and that its numerical solutions faithfully reproduce the Speedy-Angell and Poole pictures.

Editorial extensions

If this is right

  • The liquid-liquid critical point, if present, should exhibit inversion-like thermodynamic responses similar to those in gas throttling.
  • The stability-limit and liquid-liquid critical point descriptions of supercooled water can be recovered within a single model framework.
  • The same inversion analogy extends the critical point phenomenology to black hole systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The analogy might permit estimating the critical point coordinates in water from known inversion data on gases.
  • The approach could generalize to other liquids showing density or compressibility anomalies.
  • Experimental searches for the critical point could target regions where inversion thermodynamics predicts specific heat capacity or expansivity behaviors.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces a model of water that contemplates true supercooled-liquid states metastable with respect to the crystalline-solid ones. Its numerical solutions reproduce the Speedy-Angell stability-limit picture and Poole et al.'s metastable liquid-liquid criticality. The real existence of a liquid-liquid critical point is argued to gain significant theoretical plausibility from a hitherto unnoticed analogy with the inversion thermodynamics of the Joule-Thomson gas throttling process and, by extension, with equivalent phenomenology in black holes.

Significance. If the analogy is shown to rest on a rigorous structural mapping (rather than qualitative resemblance) that independently supports the LLCP, the work could strengthen the theoretical case for liquid-liquid criticality in supercooled water by linking it to established thermodynamic features of gases and gravitational systems. The reproduction of the Speedy-Angell and Poole pictures is a positive feature, but the central novelty claim depends on the analogy's independence from the model's fitted behavior.

major comments (1)
  1. [Abstract] Abstract: The claim that the LLCP 'gains significant theoretical plausibility' from the analogy with Joule-Thomson inversion thermodynamics is not accompanied by evidence of a structural mapping. No indication is given that the model's equation of state or free-energy functional possesses an inversion curve (or equivalent extremum) whose existence is mathematically tied to the LLCP in the same way the JT inversion curve is tied to the van der Waals critical point. Without this derivation, the analogy remains qualitative and does not confer independent plausibility on the central claim.
minor comments (1)
  1. The abstract refers to 'numerical solutions' reproducing known pictures but provides no information on the model's functional form, free parameters, or validation against simulation data; the main text should include these details for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the single major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the LLCP 'gains significant theoretical plausibility' from the analogy with Joule-Thomson inversion thermodynamics is not accompanied by evidence of a structural mapping. No indication is given that the model's equation of state or free-energy functional possesses an inversion curve (or equivalent extremum) whose existence is mathematically tied to the LLCP in the same way the JT inversion curve is tied to the van der Waals critical point. Without this derivation, the analogy remains qualitative and does not confer independent plausibility on the central claim.

    Authors: We agree with the referee that the manuscript presents the analogy with Joule-Thomson inversion thermodynamics (and black-hole phenomenology) as a qualitative parallel without deriving a rigorous structural mapping or demonstrating that the model's free-energy functional possesses an inversion curve mathematically linked to the LLCP in the same manner as for the van der Waals gas. The analogy is noticed and discussed as an interesting thermodynamic resemblance, but it does not rest on an independent mathematical equivalence that would confer additional plausibility beyond the model's own solutions. We will therefore revise the abstract to remove the phrasing that the LLCP 'gains significant theoretical plausibility' from the analogy and will instead describe the parallel as a noteworthy qualitative connection that may warrant further investigation. A clarifying sentence will also be added in the main text. This is a partial revision: we retain the observation of the analogy but temper the claim regarding its implications. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; central claim rests on presented analogy without reduction to inputs.

full rationale

The paper introduces a model of supercooled water whose numerical solutions are stated to reproduce the Speedy-Angell stability-limit picture and Poole et al. liquid-liquid criticality. The load-bearing claim for real existence of the LLCP is an analogy to Joule-Thomson inversion thermodynamics and black-hole phenomenology, described as 'hitherto unnoticed.' No equations, self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior work are quoted in the provided text. The derivation chain does not reduce any prediction to its own inputs by construction; the analogy supplies independent content whose structural mapping is asserted rather than shown to be tautological. This is the normal case of a self-contained model plus external analogy.

Assumptions & free parameters 0 free parameters · 0 assumptions · 1 invented entities

Abstract-only review; no specific free parameters, axioms, or invented entities can be extracted beyond the model itself being postulated to allow metastable supercooled states.

invented entities (1)
  • The model of water
    purpose: To contemplate true supercooled-liquid states metastable with respect to crystalline solids
    Introduced to enable numerical reproduction of stability-limit and liquid-liquid criticality pictures.

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Cite this review

Pith. "Pith review of Theory of supercooled water." pith.science (2026). https://pith.science/paper/VI642PJG

@misc{pith2026260524105,
  author       = {Pith},
  title        = {Pith review of: Theory of supercooled water},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VI642PJG}},
  note         = {Machine review of arXiv:2605.24105}
}
read the original abstract

We introduce a model of water contemplating true supercooled-liquid states that, as such, are metastable with respect to the crystalline-solid ones. Its numerical solutions reproduce from Speedy-Angell's stability-limit picture to Poole et al.'s metastable liquid--liquid criticality. The real existence of a liquid--liquid critical point is found to gain significant theoretical plausibility from a hitherto unnoticed analogy with the ``inversion thermodynamics'' of Joule-Thomson gas throttling process and, by extension, with the equivalent phenomenology exhibited by black holes.

Figures

Figures reproduced from arXiv: 2605.24105 by the authors.

Figure 1
Figure 1. FIG. 1: Two-dimensional illustration of individual cell states [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Numerical results for our five-state model with parameter setting “1.” (Left) Pressure [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Numerical results for our five-state model with pa [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Its upper left panel illustrates water’s unusual [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 4
Figure 4. Figure 4: FIG. 4: (Left) Molecular simulation results for the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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