Large temperature-up-jump simulations of a binary Lennard-Jones system

Aude Y. Amari; Jeppe C. Dyre; Lorenzo Costigliola

arxiv: 2601.17996 · v3 · submitted 2026-01-25 · ❄️ cond-mat.soft · cond-mat.dis-nn· cond-mat.mtrl-sci

Large temperature-up-jump simulations of a binary Lennard-Jones system

Aude Y. Amari , Lorenzo Costigliola , Jeppe C. Dyre This is my paper

Pith reviewed 2026-05-16 11:23 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nncond-mat.mtrl-sci

keywords physical agingmaterial timeTool-NarayanaswamyLennard-Jones liquidtemperature up-jumpspotential energyautocorrelation functions

0 comments

The pith

The Tool-Narayanaswamy material-time prediction collapses autocorrelation functions better after moderate temperature up-jumps than after large ones in a binary Lennard-Jones liquid.

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

This paper uses molecular dynamics to track physical aging in a binary Lennard-Jones liquid after sudden temperature increases from equilibrated low-temperature states. It first verifies that the triangular relation for potential energy remains accurate, which permits definition of a single global material time ξ. The central test then checks whether five different time-autocorrelation functions all depend only on differences in this material time. The functions align onto a master curve for the 0.43 to 0.48 jump but show clear deviations for the larger 0.37 to 0.48 jump, supporting the view that the formalism works best when the system stays relatively close to equilibrium.

Core claim

The triangular relation of the potential energy is well obeyed, allowing definition of a potential-energy-based material time ξ. The TN material-time prediction that all time-autocorrelation functions collapse to depend only on the material-time difference ξ₂ − ξ₁ is found to work better for the 0.43 to 0.48 temperature jump than for the 0.37 to 0.48 jump.

What carries the argument

The potential-energy-based material time ξ defined from the triangular relation of the potential energy, used to rescale time in aging curves.

If this is right

The triangular relation holds after both moderate and large jumps, enabling a global material time.
All five monitored quantities follow the material-time scaling for the smaller temperature jump.
The formalism performs best when the system is never very far from equilibrium.
The results are consistent with the general understanding that TN aging works well only for moderate deviations from equilibrium.

Where Pith is reading between the lines

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

Allowing each observable its own material time might restore collapse for larger jumps.
A locally defined material time could better capture dynamic heterogeneity after large jumps.
The same protocol could be tested on other glass formers to check whether the moderate-jump preference is universal.

Load-bearing premise

The triangular relation for potential energy remains accurate enough to define a single global material time even after large temperature jumps that take the system far from equilibrium.

What would settle it

Failure of the self-intermediate scattering function or mean-square displacement to collapse onto a single master curve when plotted against material-time difference for the 0.43 to 0.48 jump would disprove the central claim.

Figures

Figures reproduced from arXiv: 2601.17996 by Aude Y. Amari, Jeppe C. Dyre, Lorenzo Costigliola.

**Figure 1.** Figure 1: FIG. 1: Physical aging. (a) Schematic drawing of a temperature up jump starting and ending in thermal equilibrium [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2: Parametric representation of the triangular relation, Eq. (2). (a) Illustration of the sampling of time triplets [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Numerical test of the triangular relation Eq. (2). [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: reports the results of our simulations for temperature up jumps from T = 0.43 and T = 0.37 to T = 0.48. The left two columns show the time-autocorrelation functions during aging plotted as functions of t2 − t1 with the smaller jump to the left, parametrized by the waiting time t1. As expected, curve collapse is not observed for any of the five quantities. Instead a general speed up is seen, with the short-… view at source ↗

read the original abstract

This paper presents simulations of the physical aging of a binary Kob-Andersen-type Lennard-Jones liquid following large temperature up-jumps from equilibrated states of high relaxation time. The purpose is to investigate how well the Tool-Narayanaswamy (TN) material-time concept works for this rather extreme case of aging. First the triangular relation of the potential energy is investigated. This is found to be well obeyed, making it possible to define a potential-energy-based material time $\xi$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37 (primarily), monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility $\chi_4$, and the non-Gaussian parameter $\alpha_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference $\xi_2-\xi_1$. This is found to work better for the $0.43\to 0.48$ temperature jump than for the $0.37\to 0.48$ jump. Our findings thus confirm the general understanding that the TN aging formalism works best for systems that are never very far from equilibrium. This raises two questions for future work: Is the collapse significantly improved if each aging quantity is allowed its own material time? Can better collapse be obtained if the material-time is generalized to be locally defined (in order to reflect dynamic heterogeneity)?

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

The paper shows TN material time collapses aging data better for moderate (0.43 to 0.48) than large (0.37 to 0.48) up-jumps in the Kob-Andersen LJ system, with the triangular relation holding well enough to define a global ξ.

read the letter

The main takeaway is that the Tool-Narayanaswamy material time works better for the smaller temperature up-jump than the larger one in this standard binary Lennard-Jones glass model. The simulations confirm the potential-energy triangular relation holds, which lets them define a single material time ξ from the energy, then test whether five different observables collapse when plotted against ξ differences during aging to the final temperature 0.48. The collapse is tighter for the 0.43 to 0.48 jump than for 0.37 to 0.48, which lines up with the expectation that TN works best when the system does not stray too far from equilibrium. This is a direct, quantitative check on an existing framework rather than a new derivation. The paper does the basics cleanly: it verifies the triangular relation first, tracks potential energy, self-intermediate scattering function, mean-square displacement, χ4, and the non-Gaussian parameter α2, and reports the degradation in collapse quality for the bigger jump. The trends are consistent and the authors are straightforward about what this implies for future work on per-observable times or local definitions. The simulations follow standard protocols for the model, so the evidence is internally consistent. The soft spots are modest. There are no error bars on the collapse quality, which makes it harder to judge how large the difference really is between the two jumps. The paper also does not release code or raw data, so independent re-runs would take extra effort. The jumps tested are still within the range where the system stays reasonably close to equilibrium, so this is an incremental rather than extreme test. Overall this is the kind of careful simulation study that researchers working on physical aging in glasses will find useful as a data point on the limits of the TN picture in a well-studied model. It deserves peer review because the central claim is supported by the reported trends and the work is grounded enough to be worth referee time.

Referee Report

0 major / 2 minor

Summary. The paper reports MD simulations of physical aging in a binary Kob-Andersen Lennard-Jones liquid after large temperature up-jumps from equilibrated initial states at T=0.43 and T=0.37 to a final T=0.48. It first verifies that the potential energy obeys the triangular relation to within simulation accuracy, permitting definition of a single global material time ξ based on potential energy. It then monitors five observables (potential energy, self-intermediate scattering function, mean-square displacement, χ4, and α2) during aging and tests the TN prediction that all time-autocorrelation functions collapse onto curves depending only on the material-time difference ξ2−ξ1. The collapse is reported to be visibly better for the smaller (0.43→0.48) jump than for the larger (0.37→0.48) jump, consistent with the expectation that the TN formalism works best near equilibrium.

Significance. If the reported trends hold, the work supplies concrete numerical evidence on the range of validity of the Tool-Narayanaswamy material-time concept under large temperature jumps. The explicit comparison of collapse quality between two jump sizes quantifies how far from equilibrium the formalism remains useful and identifies two concrete directions for improvement (quantity-specific material times and locally defined material times). The independent verification of the triangular relation for potential energy provides a reproducible foundation for the material-time construction.

minor comments (2)

[Results on collapse of dynamical quantities] The quality of the data collapse onto ξ is assessed visually; no quantitative metric (e.g., mean-squared deviation from a master curve or χ² per degree of freedom) or error bars on the collapse residuals are reported, which would allow a statistically grounded comparison between the two jumps.
[Section on triangular relation] The manuscript does not state whether alternative choices for the material-time variable (e.g., based on pressure or on a different observable) were tested before settling on potential energy; an explicit statement that the triangular relation was checked for other quantities would strengthen the justification for the chosen definition of ξ.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment. The referee summary correctly describes the simulations of physical aging in the binary Lennard-Jones liquid after large temperature up-jumps and the testing of the Tool-Narayanaswamy material-time concept. We appreciate the recognition of the significance of our findings in quantifying the range of validity of the TN formalism. As no specific major comments requiring changes were provided, we do not propose any revisions.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper first verifies the triangular relation for potential energy directly in the simulations and uses the verified relation to define the material time ξ. The central test—whether autocorrelation functions collapse as a function of ξ differences—is then performed as an independent empirical comparison against this externally constructed time coordinate. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation; the collapse quality is reported as a simulation outcome that can be falsified by the data. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the triangular relation for potential energy being accurate enough to serve as a global material time. No new entities are postulated. The only free parameters are the simulation temperatures and the standard Lennard-Jones interaction parameters, both taken from prior literature.

free parameters (2)

Final temperature 0.48
Chosen as the target aging temperature; the collapse quality is reported relative to this value.
Initial temperatures 0.43 and 0.37
Selected to produce moderate and large jumps; the difference in collapse performance is the main result.

axioms (2)

domain assumption The triangular relation for potential energy holds for the chosen temperature jumps.
Invoked to define the material time ξ; verified numerically but treated as a prerequisite for the TN test.
standard math Standard molecular-dynamics assumptions (Newtonian dynamics, periodic boundaries, Nose-Hoover thermostat).
Implicit in all simulation results; no deviations reported.

pith-pipeline@v0.9.0 · 5596 in / 1607 out tokens · 29527 ms · 2026-05-16T11:23:17.917655+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference ξ2−ξ1. This is found to work better for the 0.43→0.48 temperature jump than for the 0.37→0.48 jump.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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[1] [1]

The (normalized) potential-energy time-autocorrelation functionC uu(t1, t2) defined in Eq. (4)

work page

[2] [2]

The incoherent intermediate scattering functionF s(t1, t2) calculated from the particle displacement from time t1 to timet 2, evaluated at the wavevector corresponding to the first maximum of the radial distribution function determined at the final temperature 0.48 (the peak position was virtually constant throughout all simulations), Fs(t1, t2) = * 1 NA ...

work page

[3] [3]

The mean-square displacement between timest 1 andt 2, ∆r2 (t1, t2) = * 1 NA NAX i=1 (ri(t2)−r i(t1))2 + .(6)

work page

[4] [4]

The dynamic susceptibilityχ 4(t1, t2) quantifying the degree of dynamic heterogeneity in terms of the variance of the incoherent intermediate scattering function [33], χ4(t1, t2, q) =N A "* 1 NA NAX i=1 cos(q·(r i(t2)−r i(t1) !2+ −F 2 s (t1, t2) # ; (7)

work page

[5] [5]

self-catalyzed

The non-Gaussian parameterα 2(t1, t2) (which is zero for Gaussian diffusion), α2(t1, t2) = 3 (∆r)4(t1, t2) 5 ⟨(∆r)2(t1, t2)⟩ 2 −1.(8) 8 0.00 0.25 0.50 Cuu(t1, t2) (a) T0.43→0.48 (b) T0.37→0.48 0.0 0.5 Fs(t1, t2) (c) (d) 10□2 10□1 100 101 ⟨(∆r)2⟩(t1, t2) (e) (f) 100 102 χ4(t1, t2) (g) (h) 100 102 10410□2 10□1 100 101 α2(t1, t2) (i) 100 102 104 (j) 100 102 ...

work page

[6] [6]

Mazurin, Relaxation phenomena in glass, J

O. Mazurin, Relaxation phenomena in glass, J. Non-Cryst. Solids25, 129 (1977)

work page 1977

[7] [7]

G. W. Scherer,Relaxation in Glass and Composites(Wiley, New York, 1986)

work page 1986

[8] [8]

Hecksher, N

T. Hecksher, N. B. Olsen, K. Niss, and J. C. Dyre, Physical aging of molecular glasses studied by a device allowing for rapid thermal equilibration, J. Chem. Phys.133, 174514 (2010)

work page 2010

[9] [9]

Hecksher, N

T. Hecksher, N. B. Olsen, and J. C. Dyre, Communication: Direct tests of single-parameter aging, J. Chem. Phys.142, 241103 (2015)

work page 2015

[10] [10]

Mehri, T

S. Mehri, T. S. Ingebrigtsen, and J. C. Dyre, Single-parameter aging in a binary Lennard-Jones system, J. Chem. Phys. 154, 094504 (2021)

work page 2021

[11] [11]

Riechers, L

B. Riechers, L. A. Roed, S. Mehri, T. S. Ingebrigtsen, T. Hecksher, J. C. Dyre, and K. Niss, Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time, Sci. Adv.8, eabl9809 (2022)

work page 2022

[12] [12]

K. Moch, C. Gainaru, and R. B¨ ohmer, Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener–Volterra approach and extended Tool–Narayanaswamy–Moynihan models, J. Chem. Phys.161, 014502 (2024)

work page 2024

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O. S. Narayanaswamy, A model of structural relaxation in glass, J. Amer. Ceram. Soc.54, 491 (1971). 10

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M. Micoulaut, Relaxation and physical aging in network glasses: a review, Rep. Prog. Phys.79, 066504 (2016)

work page 2016

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I. M. Hodge, Physical aging in polymer glasses, Science267, 1945 (1995)

work page 1945

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J. M. Hutchinson, Physical aging of polymers, Prog. Polym. Sci.20, 703 (1995)

work page 1995

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Cangialosi, V

D. Cangialosi, V. M. Boucher, A. Alegria, and J. Colmenero, Physical aging in polymers and polymer nanocomposites: recent results and open questions, Soft Matter9, 8619 (2013)

work page 2013

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G. B. McKenna and S. L. Simon, 50th anniversary perspective: Challenges in the dynamics and kinetics of glass-forming polymers, Macromolecules50, 6333 (2017)

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B. Ruta, E. Pineda, and Z. Evenson, Relaxation processes and physical aging in metallic glasses, J. Phys.: Condens. Matter 29, 503002 (2017)

work page 2017

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L. Song, W. Xu, J. Huo, F. Li, L.-M. Wang, M. D. Ediger, and J.-Q. Wang, Activation entropy as a key factor controlling the memory effect in glasses, Phys. Rev. Lett.125, 135501 (2020)

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J. C. Mauro,Materials Kinetics: Transport and Rate Phenomena(Elsevier, Amsterdan, Netherlands, 2021)

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Vila-Costa, M

A. Vila-Costa, M. Gonzalez-Silveira, C. Rodriguez-Tinoco, M. Rodriguez-Lopez, and J. Rodriguez-Viejo, Emergence of equilibrated liquid regions within the glass, Nat. Phys.19, 114 (2023)

work page 2023

[23] [23]

Henot, X

M. Henot, X. A. Nguyen, and F. Ladieu, Crossing the frontier of validity of the material time approach in the aging of a molecular glass, J. Phys. Chem. Lett.15, 3170 (2024)

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