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arxiv: 2307.10143 · v2 · pith:5OUKEKOXnew · submitted 2023-07-19 · ❄️ cond-mat.soft · cond-mat.dis-nn· cond-mat.mtrl-sci

Starting from the amorphous ground state: linking landscape thermodynamics to slow dynamics and crossover

Anshul D. S. Parmar , Simon G. Kellers , Andreas Heuer This is my paper

Pith reviewed 2026-05-25 08:31 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nncond-mat.mtrl-sci
keywords fragile-to-strong crossoverpotential energy landscapeconfigurational entropyglass transitioninherent structuresswap Monte Carlotrap model
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The pith

Depletion of low-energy states in the potential energy landscape produces the fragile-to-strong crossover.

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

The paper establishes that a finite system size can be identified for a model glass former that allows both bulk-like behavior above Tg/2 and complete enumeration of the PEL to its lowest amorphous states using swap Monte Carlo. This enables direct computation of the configurational entropy over the full temperature range, showing a depletion of low-energy states that deviates from Gaussian statistics and controls the low-temperature entropy curvature. The apparent activation energy for diffusivity tracks the mean inherent structure energy, leading to a gradual crossover to Arrhenius behavior. This is explained by a trap model of the PEL in which the FSC arises naturally from the depletion and the lower bound of the landscape. The binomial PEL model further shows that the crossover is observable only when the depletion regime is reached in the temperature window studied. A reader would care because this provides a parameter-free microscopic origin for the FSC tied to the bounded nature of the energy landscape.

Core claim

Using swap Monte Carlo combined with full PEL analysis, we obtain equilibrium data deep into the glassy regime in a finite system that reproduces bulk behaviour for T ≳ Tg/2. We find a pronounced depletion of low-energy states relative to the Gaussian regime of the PEL, which governs the low-temperature curvature of the configurational entropy. The apparent activation energy of the diffusivity closely follows the temperature dependence of the mean inherent structure energy and exhibits a gradual crossover towards Arrhenius-like behaviour. This correlation is consistent with a trap-model description of the PEL, in which the FSC emerges naturally as a consequence of the depletion of low-energy

What carries the argument

Depletion of low-energy states relative to the Gaussian regime of the PEL and the resulting lower bound, which sets the low-T curvature of configurational entropy in a trap-model description.

If this is right

  • The apparent activation energy of diffusivity follows the temperature dependence of the mean inherent structure energy.
  • The FSC emerges as a natural consequence of the depletion of low-energy states and the lower bound of the PEL.
  • The observability of the FSC depends on whether the depletion regime is reached within the accessible temperature window, as shown by the binomial model.

Where Pith is reading between the lines

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

  • This mechanism suggests that the FSC should be more pronounced in systems where the Gaussian approximation fails at higher temperatures.
  • The approach of exhaustive PEL sampling could be applied to other models to test if the same depletion mechanism governs their dynamics.
  • If the lower bound is the key, then modifying the model to have deeper states might shift or eliminate the crossover.

Load-bearing premise

A single finite system size simultaneously reproduces bulk thermodynamic and dynamic behaviour for T ≳ Tg/2 while permitting exhaustive sampling of the PEL down to its lowest-energy amorphous states.

What would settle it

If in a larger system the low-energy depletion is not observed or the activation energy does not track the mean inherent structure energy despite the presence of a FSC, the proposed connection would be falsified.

Figures

Figures reproduced from arXiv: 2307.10143 by Andreas Heuer, Anshul D. S. Parmar, Simon G. Kellers.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (c&d). Here we show the actual distributions at different sizes N and their prediction via the superpo￾sition hypothesis, based on the distribution at size N/2 (see Methods). The temperatures are chosen far below Tg. For the transition from N = 33 to N = 66, we see a very good agreement for higher energies, whereas deviations are visible on the low-energy side. This was expected due to the shifted bottom o… view at source ↗
Figure 3
Figure 3. Figure 3: b shows the configurational entropy for various system sizes. For N = Nc = 66 its temperature de￾pendence, involving a transition from positive to nega￾tive curvature at low but finite temperature (see also SI (IX)), reflects the low-energy state depletion, including the cutoff. For the present model glass, it stems a unique footing to quantify Kauzmann’s picture of entropy cri￾sis [28] and provides a dire… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

A microscopic understanding of low-temperature thermodynamics and its relation to dynamical features such as a fragile-to-strong crossover (FSC) remains a central challenge in glass physics. Using swap Monte Carlo combined with a full potential-energy-landscape (PEL) analysis of a non-network-forming model, we obtain equilibrium data deep into the glassy regime and identify a finite system size that simultaneously reproduces bulk behaviour for $T \gtrsim T_g/2$ and allows complete sampling of the PEL down to its lowest-energy amorphous states. This enables the direct computation of the configurational entropy over the full temperature range of the finite system without relying on liquid-state thermodynamic integration. We find a pronounced depletion of low-energy states relative to the Gaussian regime of the PEL, which governs the low-temperature curvature of the configurational entropy. Numerically, the apparent activation energy of the diffusivity closely follows the temperature dependence of the mean inherent structure energy and exhibits a gradual crossover towards Arrhenius-like behaviour. This correlation is consistent with a trap-model description of the PEL, in which the FSC emerges naturally as a consequence of the depletion of low-energy states and thus of the lower bound of the PEL. We further argue, as illustrated analytically for a simple binomial model of the PEL, that the observability of a FSC depends on whether the depletion regime is reached within the accessible temperature window.

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

1 major / 0 minor

Summary. The manuscript investigates the connection between the potential energy landscape (PEL) structure and the fragile-to-strong crossover (FSC) in glass-forming liquids. Using swap Monte Carlo simulations combined with exhaustive PEL enumeration on a finite system of a non-network-forming model, the authors identify a system size that matches bulk behavior above Tg/2 and allows complete sampling down to the lowest amorphous states. They compute the configurational entropy directly, observe depletion of low-energy states, and show that the apparent activation energy of diffusivity correlates with the mean inherent structure energy, leading to a crossover to Arrhenius behavior. This is interpreted through a trap model, with an analytic binomial PEL model illustrating the conditions for observing the FSC.

Significance. If the finite-size validation holds and the correlations are robust, this provides a microscopic explanation for the FSC arising directly from depletion of low-energy states and the PEL lower bound. The direct computation of configurational entropy over the full range without liquid-state integration, the numerical correlation between activation energy and mean inherent-structure energy, and the parameter-free analytic binomial illustration are notable strengths that could advance trap-model interpretations of glassy dynamics.

major comments (1)
  1. [Abstract, paragraph 2] Abstract, paragraph 2: The central claim that a single finite system size N simultaneously reproduces bulk thermodynamic and dynamic behaviour for T ≳ Tg/2 while permitting exhaustive sampling of the PEL down to its lowest-energy amorphous states is load-bearing for the interpretation. No quantitative validation is described showing that diffusivity or relaxation times from this N match those of larger systems in the overlapping temperature window; without such checks, finite-size rounding of the PEL or altered barrier statistics could produce an apparent depletion and crossover that does not survive in the thermodynamic limit.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. The concern about finite-size validation of dynamics is well taken and we address it directly below.

read point-by-point responses

  1. Referee: [Abstract, paragraph 2] Abstract, paragraph 2: The central claim that a single finite system size N simultaneously reproduces bulk thermodynamic and dynamic behaviour for T ≳ Tg/2 while permitting exhaustive sampling of the PEL down to its lowest-energy amorphous states is load-bearing for the interpretation. No quantitative validation is described showing that diffusivity or relaxation times from this N match those of larger systems in the overlapping temperature window; without such checks, finite-size rounding of the PEL or altered barrier statistics could produce an apparent depletion and crossover that does not survive in the thermodynamic limit.

    Authors: We agree that explicit quantitative checks on dynamics are necessary to support the claim. The manuscript validates thermodynamic quantities (configurational entropy, mean inherent-structure energy) against larger N in the T ≳ Tg/2 window, but does not present corresponding diffusivity or relaxation-time comparisons. In the revised manuscript we will add these comparisons, using additional swap-MC runs on larger systems where computationally feasible, to demonstrate that the chosen N reproduces bulk-like dynamics within statistical error above Tg/2. This will directly address the possibility of finite-size effects on barrier statistics. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct PEL enumeration and independent analytic illustration

full rationale

The derivation computes depletion of low-energy states and configurational entropy directly via exhaustive inherent-structure enumeration on a selected finite system, then observes that diffusivity activation energy tracks mean inherent-structure energy. The trap-model description is invoked only as a post-hoc consistency check ('consistent with a trap-model description'), not as the source of the depletion or the FSC. The binomial model is explicitly an 'analytic illustration' separate from the simulation data. No self-citations, fitted parameters renamed as predictions, or self-definitional steps appear in the abstract or described chain. The finite-size choice is an assertion about representativeness but does not reduce any equation to its own input by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a finite system size that simultaneously satisfies bulk reproduction and exhaustive PEL sampling, plus standard statistical-mechanical relations between PEL enumeration and configurational entropy; no new particles or forces are introduced.

free parameters (1)
  • finite system size N
    Selected so that the model reproduces bulk behaviour for T ≳ Tg/2 while still allowing complete sampling of the PEL to its lowest states.
axioms (2)
  • domain assumption Configurational entropy can be obtained by direct enumeration of inherent structures in the PEL without thermodynamic integration from the liquid
    Invoked to justify computing entropy over the full temperature range of the finite system.
  • standard math Standard assumptions of classical statistical mechanics relating inherent-structure energies to thermodynamic quantities
    Used throughout the PEL analysis.

pith-pipeline@v0.9.0 · 5791 in / 1541 out tokens · 27798 ms · 2026-05-25T08:31:47.033224+00:00 · methodology

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Reference graph

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