[Paper Review] Large temperature-up-jump simulations of a binary Lennard-Jones system

Aude Amari, Lorenzo Costigliola+1 more|arXiv (Cornell University)|Jan 25, 2026

Material Dynamics and Properties0 citations

TL;DR

The paper tests the Tool-Narayanaswamy material-time aging description for a binary Kob–Andersen–type Lennard-Jones liquid subjected to large temperature up-jumps, using simulations to assess collapse of time-correlation functions onto material-time differences.

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 studied. This is found to be well obeyed, making it possible to define a potential-energy-based material time $ξ$. We proceed to study aging toward equilibrium at the final temperature 0.48 for jumps from the two temperatures 0.43 and 0.37, monitoring the following five quantities: the potential energy, the self-intermediate scattering function, the mean-square displacement, the dynamic susceptibility $χ_4$, and the non-Gaussian parameter $α_2$. The TN material-time prediction is that all time-autocorrelation functions should collapse to only depend on the material-time difference $ξ_2-ξ_1$. This is found to work better for the $0.43 o 0.48$ temperature jump than for the $0.37 o 0.48$ jump, however. 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)?

Motivation & Objective

• Assess whether a single material time, derived from potential energy, can linearize aging after large temperature up-jumps.
• Evaluate the triangular relation (CK time-reparametrization) for the potential-energy autocorrelation during aging.
• Test collapse of multiple time-autocorrelation functions (five observables) onto the material-time difference.
• Compare aging behavior for a small vs. large up-jump to final temperature and assess limits of TN aging description.

Proposed method

• Use a binary Lennard-Jones mixture (80% A, 20% B) with shifted-force cutoffs and simulate with GPU-optimized code RUMD.
• Define material time xi(t) from the potential-energy autocorrelation via Cuu(t1,t2)=phi_eq(xi(t2)-xi(t1)).
• Validate the CK triangular relation C13=F_A(C12,C23) by looping over millions of time triplets after a temperature up-jump.
• Monitor five quantities during aging: Cuu, Fs, <Delta r^2>, chi4, and alpha2 across jumps from T=0.43 and T=0.37 to T=0.48.
• Assess collapse of these observables when plotted against xi2−xi1 rather than t2−t1.
• Compare results for small and large up-jumps.

Figure 1 : Physical aging. (a) Schematic drawing of a temperature up jump starting and ending in thermal equilibrium (with time on the x-axis). Even though not all quantities relax in identical manner, the standard TN aging formalism operates with a single “global” clock controlling all relaxations

Experimental results

Research questions

• RQ1 Does a single TN material time derived from potential energy adequately describe aging after large temperature up-jumps in a Kob–Andersen–type LJ liquid?
• RQ2 How well does the CK triangular relation hold for the potential-energy autocorrelation under aging after up-jumps?
• RQ3 Can multiple dynamical observables collapse onto a universal function of material-time difference, and does collapse depend on jump size?
• RQ4 Are local or multiple material times needed to describe aging when jumps are large?

Key findings

• The triangular relation is obeyed well for potential-energy autocorrelations, enabling a material time based on the potential energy.
• Aging observables collapse better for the smaller up-jump (0.43→0.48) than for the larger jump (0.37→0.48) when using a common material time.
• For the smaller jump, Cuu and Fs show strong collapse; MSD, chi4, and alpha2 show weaker but partial collapse.
• For the larger jump, none of the five observables show convincing collapse with a single material time, indicating limits of single-clock TN aging.
• The material time becomes proportional to real time at long times as equilibrium at the final temperature is approached; short times show deviations.
• The authors suggest that either each observable could have its own material time or local material times might be needed in the presence of dynamic heterogeneity.

Figure 2 : Parametric representation of the triangular relation, Eq. ( 2 ). (a) Illustration of the sampling of time triplets used to calculate correlation “triangles”. The values on the time axis illustrate the logarithmic increase in time intervals within a single simulation block. (b) Illustratio