Glassy Signatures in Water's Second Liquid

Ali Hassanali; Florian Pabst

Glassy Signatures in Water's Second Liquid

T0 review · 4 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read What is often interpreted as water's liquid-liquid transition is actually the onset of glassy arrest, with a glass-transition temperature near 189 K.

desk verdict Strong qualitative case for glassy arrest behind water's apparent LLT; the 189 K Tg is a plausible but under-supported extrapolation. read the letter →

arxiv 2604.00794 v3 pith:HSJHMTOB submitted 2026-04-01 cond-mat.soft

Florian Pabst , Ali Hassanali This is my paper · ORCID

classification cond-mat.soft

keywords supercooledwaterglasstransitionliquid-liquidkineticarrestVogel-Fulcher-Tammannequationdielectricrelaxationtwo-statefluctuationsmachine-learningpotentials

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

This paper argues that the long-sought liquid-liquid transition in supercooled water is not a transition between two equilibrium liquids. The features commonly read as evidence of a second low-density liquid—energy fluctuations, two-state switching, a low-q scattering response—coincide with periods of near-zero molecular mobility, meaning the low-density state is a kinetically arrested glass. By extrapolating well-equilibrated dielectric relaxation times with the Vogel-Fulcher-Tammann equation, the authors obtain an ambient-pressure glass-transition temperature of 189 ± 8 K, squarely in the range where a liquid-liquid transition has been proposed. If correct, water's celebrated two-state phenomenology would be the boundary between an ergodic liquid and a non-ergodic glass, not a hidden critical point.

What carries the argument

The load-bearing tool is the Vogel-Fulcher-Tammann fit to dielectric relaxation times (obtained from the total dipole autocorrelation), which extrapolates simulated dynamics—covering roughly 10^-9 to 10^-6 s—to the conventional glass-transition definition tau = 100 s. Supporting measures include time-resolved mean-square displacement to identify dynamical arrest, pressure/cooling ramps that generate rate-dependent glassy states, and isochronal lines (equal-relaxation-time contours) that map the non-ergodic boundary in the pressure-temperature plane. The temperature at which relaxation time varies most steeply with pressure, near 193.5 K, coincides with the onset of the purported two-state fl

What would settle it

Measure structural relaxation times of pure bulk water at ambient pressure down to ~185 K using an ultrafast probe that outruns crystallization; if the relaxation time at 189 K remains many orders of magnitude below the 100-s mark—i.e., the liquid is still mobile—the inferred Tg and the glass-LLT identification would be refuted.

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Extended reading notes

Core claim

The central claim is that the purported low-density liquid (LDL) phase of supercooled water is dynamically arrested rather than liquid: in trajectories where LDL-HDL fluctuations were previously reported, the low-energy state shows essentially flat time-resolved mean-square displacement, indicating vanishing diffusion over hundreds of nanoseconds. Pressure- and temperature-ramp simulations show classic glassy signatures—rate-dependent final energies, physical aging, a step-like then peak-like heat capacity—and the onset of kinetic arrest coincides with the heat-capacity maximum. VFT extrapolation of dielectric relaxation times to tau = 100 s yields Tg = 189 ± 8 K at ambient pressure across t

Load-bearing premise

The central number rests on assuming the Vogel-Fulcher-Tammann equation fitted to relaxation times spanning only about a microsecond continues to hold across the roughly eight orders of magnitude needed to reach the 100-second definition of the glass transition, with no change in relaxation mechanism.

Editorial extensions

If this is right

The low-density 'second liquid' would not exist as an equilibrium phase; simulated HDL-LDL coexistence reflects intermittent trapping in a glassy state.
Free-energy calculations that sample the low-density state would be biased by incomplete equilibration, so computed LLT free-energy differences need revisiting.
Experimental signatures—low-q scattering, sharp heat-capacity peaks, Widom-line-like response maxima—appear where dynamics turn non-ergodic and do not require a hidden critical point.
Water's ambient-pressure glass transition would be near 189 K rather than 136 K, reconciling confinement, electron-diffraction, and minimally perturbing salt-solution measurements.
The mechanism may generalize: first-order-like coexistence between liquid and arrested states could masquerade as liquid-liquid transitions in other polyamorphic or deeply supercooled systems.

Reading between the lines

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

The maximal pressure sensitivity of relaxation near 193.5 K implies that modest pressure noise in experiments or simulations can flip small water samples across the ergodic boundary; this may explain why some ultrafast droplet experiments report two-liquid-like features while others do not.
If the glassy-arrest scenario holds, the singularity-free interpretation of water's anomalies becomes a natural framework, since sharp response-function maxima can emerge from kinetic slowing without an underlying critical point.
The supplemental barostat-dependence result suggests a concrete test: systematically varying thermostat/barostat coupling and system size should make two-state fluctuations vanish under softer pressure control, providing a falsifiable simulation benchmark.
The VFT parameters could be used to predict Tg for heavy water or for water under confinement, generating testable dielectric and NMR predictions beyond the paper's direct claims.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear Colleague,

You should know upfront: this is a paper that will get people talking. Pabst and Hassanali use three water models to argue that the supposed liquid-liquid transition in supercooled water is actually a glass transition—the low-density state is not a liquid at all but an amorphous solid that intermittently traps the system. The qualitative case is strong, and they support it with multiple independent probes: trMSD plateaus, pressure- and temperature-ramp vitrification, barostat sensitivity, and comparisons to X-ray scattering and heat capacity experiments. This is genuinely new as a systematic demonstration across ML models, and it reframes the long debate in a productive way.

Where I get uneasy is the headline number. The claim that ambient-pressure Tg = 189 ± 8 K comes from fitting VFT to dielectric relaxation times that span only ~10^-9 to 10^-6 s, then extrapolating eight orders of magnitude to tau = 100 s. The ±8 K is the spread between models, not a fit uncertainty, and no error bars are reported on the VFT parameters. At the lowest simulated temperatures the system is already close to arrest, so some of the points used in the fit may be biased by non-ergodicity. Alternative functional forms (Bässler, etc.) would give a different Tg. This is a real soft spot, and it's the load-bearing part of the quantitative conclusion. The paper would be much stronger if they released the tau(T) data and showed a stability analysis of Tg against fit choices and data range.

That said, the qualitative message does not depend on the exact Tg. The observations that two-state fluctuations coincide with kinetic arrest, that they vanish under different barostat settings, and that larger simulations don't show them are convincing. The authors are also candid about limits: they explicitly say they cannot exclude an LLT, and they note that their Tg estimate is model-dependent. That honesty helps.

I would send this to peer review. A serious referee should push on the VFT extrapolation and ask for data/code, but the core reinterpretation deserves to be aired. I'd cite the qualitative result cautiously, not the specific Tg.

Referee Report

4 major / 6 minor

Summary. The paper argues that the two-state fluctuations widely interpreted as evidence of a liquid–liquid transition (LLT) in supercooled water are instead manifestations of dynamical arrest: the low-density state is a kinetically trapped glass, not an equilibrium second liquid. Evidence includes time-resolved mean-square displacement (trMSD) plateaus in three water models (DNN@SCAN, DNN@MB-pol, TIP4P/2005), rate-dependent vitrification in pressure- and temperature-ramp simulations, barostat sensitivity of the two-state fluctuations (SM Fig. S1), and the coincidence of kinetic arrest with the heat-capacity maximum. The central quantitative claim is an ambient-pressure glass-transition temperature of 189 ± 8 K, obtained by VFT extrapolation of simulated structural relaxation times to τ = 100 s, close to the temperature range where an LLT has been proposed. The authors also construct isochronal lines in the P–T plane for the DNN@SCAN model and compare simulated relaxation times with dielectric and NMR experiments at 1 bar and 5 kbar.

Significance. If correct, the reinterpretation is significant: it would unify several experimental and simulation observations under a glass-transition framework, reducing the need for an equilibrium LLT to explain water's anomalies. The paper has notable strengths: it uses three independent models, including two advanced machine-learning potentials with explicit melting-point corrections; it directly compares with experimental dielectric, NMR, calorimetric, and X-ray data; it provides a concrete, testable prediction (a high Tg near 189 K for bulk low-density water); and it includes supplementary mechanistic checks such as barostat sensitivity and aging behavior. The manuscript is also unusually candid about its own limitations, including the extrapolative nature of the VFT fit and the small-system dependence of the apparent phase fluctuations.

major comments (4)

[§4.4 / Fig. 3C, Eq. (2)] The headline Tg = 189 ± 8 K rests on VFT extrapolation of simulated relaxation times spanning roughly 10^-9 to 10^-6 s (Fig. 3C) to τ = 100 s, an extrapolation of eight orders of magnitude. The reported ±8 K is the spread among three models, not an uncertainty on the extrapolation itself. The paper acknowledges that the open symbol in Fig. 3B is a lower bound from a partially decayed correlation function, and that low-temperature simulations may be non-ergodic. This is load-bearing because the central claim — that vitrification coincides with the proposed LLT — depends on Tg landing near 189 K. A concrete robustness test would be to report VFT fit parameters with their confidence intervals, to show χ² residuals for alternative forms (e.g., Bässler, modified VFT, or Arrhenius crossover), and to test sensitivity of Tg to excluding the lowest-temperature points or to alternative definitions
[Fig. 2E and §3.2 (SM)] The heat-capacity peak in Fig. 2E is obtained by differentiating a six-parameter empirical fit (Eq. S2) to enthalpy data from a single cooling trajectory at 2 K/ns. The fit parameters are smoothing parameters, not physical ones, and no uncertainty is provided. The claim that the Cp peak at ~243 K 'approaches' the experimental maximum at 228.9 K is presented without quantitative error bars or a rate-dependence scaling argument. This comparison is central to the argument that vitrification masks a thermodynamic divergence, so the lack of uncertainty propagation is a weakness. A simple bootstrap or multiple-trajectory estimate of the peak temperature would strengthen the claim.
[Discussion, Fig. 4] The isochronal 'phase diagram' in Fig. 4 uses VFT extrapolations (open circles) to draw isochrones out to τ = 100 s, yet the VFT parameters at each pressure are not shown, nor are the number of state points per pressure or the quality of the fits. The claim that T_max∇Pτ = 193.5 K coincides with the proposed LLT is made from this extrapolated map; without fit-quality metrics or error bars on the isochrone positions, this coincidence is not quantitatively demonstrated. Providing the fit parameters and uncertainties, or at least a table of Tg(P) values, would make the map reproducible and the claim testable.
[Fig. 1 / SM §2.1] The barostat-sensitivity result (SM Fig. S1) is a strong point: it shows that the two-state fluctuations can be eliminated by changing the damping constants. However, the claim that the original-settings trajectory 'again exhibits trapping' in the low-energy state for ~0.5 μs is based on a single trajectory at 192 molecules. Given that the authors themselves argue that small boxes amplify pressure fluctuations, the generality of the trapping phenomenon should be quantified — e.g., how many independent trajectories show how long a plateau, or how the trMSD plateau duration varies with box size. If this is not presented, the claim that apparent LLT fluctuations are generally a glass-artifact remains suggestive rather than established.

minor comments (6)

[Throughout] The notation 'DNN@SCAN' and 'DNN@MB-pol' is used inconsistently: the models are also referred to as 'SCAN@DNN' in SM §2.1. Please standardize.
[Fig. 3C legend] The legend says 'experiment: NMR, 2.8nm; DS, 1.9nm; DS, LiCl-solution' but the caption does not specify which symbols correspond to which experimental dataset, nor the temperature ranges where each dataset is valid. Adding a legend entry with symbols and a sentence about the confinement sizes would improve readability.
[Eq. (S3)] The empirical pressure fit τ(P) = a1 exp(-P/P0) + a2 + a3 P^a4 uses five parameters for three temperatures; the exponent a4 is not reported for any temperature, and the fit is stated to be 'just a guide to the eye.' Since the open symbol at 2000 bar is obtained via frequency-pressure superposition of a partially decayed spectrum, the reader should be told explicitly whether the open symbol is included in the VFT fit at 1 bar or only in the pressure fit. This affects the interpretation of the low-pressure extrapolation.
[Fig. 2A inset] The inset of Fig. 2A shows physical aging after rapid depressurization, but the axis label 'Epot / kJ/mol' is ambiguous: is this per molecule or per mole? In the main panels it is stated to be per molecule; please clarify.
[References] References 6, 7, 16, 36, 37, 46, 47 include years 2025–2026, which are plausible for a 2026 arXiv posting. However, for citations of unpublished results (e.g., Ref. 16 'Lunkenheimer, Reuter, Schulz, Wolf, Loidl, Phys. Rev. E 111(6), 065408 (2025)') the journal and year are given; please verify page/article numbers for all preprints, as some cited works appear to be very recent and not yet indexed.
[SM §4.4] The statement that 'many liquids follow the so-called two-thirds rule' is used to support Tg ≈ 182 K, but the rule is empirical and has exceptions; this is fine as a consistency check, but should be clearly labeled as 'not definitive' (which it already is, to the authors' credit). Perhaps add a sentence that the two-thirds rule for water's melting point at 273 K gives 182 K, which is within the stated uncertainty.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the glass-arrest claim rests on direct kinetic observables and external benchmarks, and the Tg value is a transparent VFT extrapolation rather than a hidden fit.

full rationale

The central interpretive claim—that the apparent low-density phase is a kinetically arrested glass—is not derived from the conclusion. It is based on independent observables: trMSD plateaus in the low-energy phase (Eq. 1 and Fig. 1), rate-dependent depressurization/cooling energies (Fig. 2A,D), and the coincidence of the Cp maximum with translational arrest (Fig. 2E,F). None of these diagnostics is defined in terms of 'glassy arrest'; flat trMSD and rate-dependent trapping are measured quantities. The quantitative Tg=189±8 K is obtained by an explicit VFT fit (Eq. 2) to dielectric relaxation times and extrapolation to tau=100 s; this is acknowledged in the text ('we estimate the experimental glass transition by extrapolating...'). The extrapolation is anchored by direct comparison with nanoconfined water, LiCl solutions, electron diffraction, and droplet Cp data (Fig. 3C and Discussion), so the number is benchmarked externally rather than forced by a pre-selected outcome. The self-citations (refs 36,47 and related methods) support auxiliary methodology—temperature-shift transferability, dielectric self/total factor, and the dipole neural network—and are corroborated by in-paper experimental comparisons; they are not load-bearing. The SM's own caveat that one extrapolated tau at 2000 bar is a lower bound (Supplemental Sec. 4.2) is an uncertainty/robustness limitation, not a circularity, because the central glass-arrest inference does not depend on that single point. No circular step can be exhibited; no fitted parameter is renamed as an independent prediction.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the fidelity of machine-learned water models and on the validity of VFT extrapolation; both are domain assumptions rather than established facts. No new physical entity is introduced. The quantitative Tg is determined by fitted VFT parameters, so the free-parameter count is modest but concentrated at the key conclusion.

free parameters (5)

VFT parameters (tau0, D, T0) per model and pressure = T0 = 184.5 K, Tg = 196.5 K for DNN@SCAN at 1 bar
Fitted to simulated dielectric relaxation times and used to extrapolate to tau = 100 s to define Tg; the central numeric result depends entirely on this fit.
Melting-point shift corrections = -40 K (DNN@SCAN), +10 K (DNN@MB-pol)
Applied to all DNN temperatures for comparison with experiment; taken from refs 21 and 22, not fitted here, but chosen by hand and directly affects the placement of Tg.
Enthalpy fit parameters (a1..a4, s, Tr) = not reported
SM Eq. S2, used to smooth H(T) for computing Cp; fitted to simulation data, uncertainty not propagated.
Pressure-fit parameters (a1..a4, P0) = not reported
SM Eq. S3, a guide-to-eye extrapolation of tau(P) for Fig. 3B; not central but used to illustrate pressure dependence.
NMR self-to-total scaling factor = 2
Applied to NMR relaxation times in Fig. 3C based on the ratio of total to self dielectric spectra (SM Fig. S4); affects the experimental comparison.

assumptions (6)

domain assumption DNN@SCAN and DNN@MB-pol potentials faithfully reproduce supercooled water structure and dynamics after a constant melting-point shift.
The entire analysis uses these ML potentials; no direct validation is shown at the deeply supercooled state points where Tg is estimated.
domain assumption The VFT equation (Eq. 2) describes structural relaxation over the extrapolation range from ~10^-9 s to 100 s.
VFT is empirical and is assumed to hold over eight orders of magnitude; several other functional forms fit glassy relaxation data equally well.
domain assumption The dielectric-loss peak frequency gives the structural alpha relaxation time of water.
The paper argues dipole fluctuations match dielectric spectroscopy, but the method assumes no significant contribution from beta relaxations or confinement artifacts in the fit window.
domain assumption Nanoconfined water and 14.8 mol% LiCl solution experiments are representative of bulk supercooled water dynamics.
Figure 3C compares simulated tau to these experiments; confinement and salt effects can shift Tg, and the LiCl solution is argued to resemble water at high pressure.
domain assumption A 512-molecule simulation box is large enough to avoid finite-size effects on relaxation times.
The authors note two-state fluctuations appear only in small systems (192 molecules) and use 512 molecules for dynamics, but no systematic finite-size convergence test is shown for tau.
domain assumption Equilibration for at least 10 tau in NPT/NVT ensures an equilibrated liquid before production.
SM Methods; if equilibration is incomplete, the VFT fit could be biased toward shorter tau, making Tg underestimated.

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Cite this review

Pith. "Pith review of Glassy Signatures in Water's Second Liquid." pith.science (2026). https://pith.science/paper/HSJHMTOB

@misc{pith2026260400794,
  author       = {Pith},
  title        = {Pith review of: Glassy Signatures in Water's Second Liquid},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HSJHMTOB}},
  note         = {Machine review of arXiv:2604.00794}
}

abstract

The origin of water's anomalous behavior remains a central open problem in the physical sciences and is often attributed to a liquid-liquid transition (LLT) between high- and low-density liquid states deep in the supercooled regime. Experimental access to this region has been challenging due to rapid crystallization, leaving atomistic simulations as a major source of supporting evidence. Using extensive machine-learning-accelerated first-principles simulations in direct comparison with spectroscopic, structural, and dynamical experimental measurements, we show that features commonly interpreted as signatures of two-liquid behavior coincide with the onset of dramatic dynamical slowing down characteristic of an emerging non-ergodic glassy state. Specifically, we find that two-state fluctuations associated with an LLT, are also consistent with a transformation from a high-density liquid to a kinetically constrained low-density glassy-like state. By mapping equilibrium dynamics across pressure and temperature, our results call for a closer examination of water's metastable landscape, in which two-state behavior may reflect a relatively high glass-transition temperature of low-density water, 189~$\pm$~8 K---curiously close to the temperature commonly associated with the proposed LLT.

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Reviewed August 2, 2026 · model on record in the stance chip above.