Persistently Non-Gaussian Metastable Liquids

TL;DR

The paper addresses persistent non-Gaussian dynamics in dense metastable liquids across thermal, externally driven, and active conditions. It develops and analyzes three amorphous models via molecular dynamics, quantifying non-Gaussianity with both conventional (alpha2) and information-theoretic (DeltaS_ng) measures, and introducing local MSD mappings and displacement statistics. The results demonstrate universal, long-lived non-Gaussian tails in particle displacements, with behavior tied to cage-breaking, plastic rearrangements, and facilitated flows, and show that negentropy provides a robust indicator of heterogeneity persistence beyond traditional moments. This work offers a unified, landscape-based view of non-equilibrium glassy dynamics and suggests information-theoretic metrics as powerful tools for characterizing and potentially controlling transport in complex materials.

Abstract

Particles undergoing Fickian diffusion within smooth energy landscapes exhibit Gaussian statistics. However, this Gaussian behavior is often elusive in complex liquids, where particle dynamics within spontaneously fluctuating or spatio-temporally heterogeneous environments lead to a breakdown of ergodicity and time-reversal symmetry. This is usually caused by extreme particle movements or sudden dynamical arrest. Such situations are prevalent in dense metastable liquids exhibiting slow flow or cooperative movements, facilitated by cage-breaking. We investigate the dynamics of glassy systems driven by either thermal, external, or environmental fluctuations. Despite their differences, our findings reveal that particle motion is universally affected by large deviations, resulting in non-Gaussian tails persisting over multiple decades in time. We further discuss the underlying dynamical aspects.

Figures (3)

• Figure 1: Dynamic heterogeneity in supercooled liquid: (a) Spatial map of particle displacements indicating heterogeneous dynamics at $T= 0.45$. Length of the arrows represents the magnitude of the displacements at single particle level in a 2D slice of the three dimensional system. (b) Mean-squared displacement as a function of time for two different temperatures as indicated. At low temperature, prominent plateau can be seen beyond the ballistic regime. At long times, the mean squared displacements grow linearly in time (shown by dotted line), although they may not be indicator of onset of Fickian-diffusion. (c,d) Distribution of particle displacements (shown with open symbols) and the corresponding nearest Gaussian constructions (shown with solid black lines) at three different time intervals as indicated; for (c) low temperature ($T=0.45$) and (d) high temperature ($T=0.70$). Both the particle distributions and its nearest Gaussian has identical first and second moments. (e,f) Measurements of Non-Gaussianity using conventional and optimal methods: conventional non-Gaussian parameter $\alpha_2$ (obtained from the ratio of the kurtosis to square of the second moment) and negentropy $\Delta S_{\rm ng}$ (obtained from the KL-divergence between the displacement distributions and its nearest Gaussian, as shown in figs. (c-d)) as a function of time for the system at temperatures $T = 0.45, 0.70$. Here, we used Model 1 to simulate these data in three dimensions for a system size $N=1000$.
• Figure 2: Plastic rearrangements as a precursor to catastrophic failure in yield stress materials : (a) Distribution of instantaneous particle displacements ($P(\Delta_{X})$) temporally close to critical failure, for an imposed shear-stress $\Sigma=0.85$ (in open symbols). The solid line shows the nearest Gaussian distribution respective to $P(\Delta_{X})$. (b) Spatial map of coarse-grained mean-squared-displacements shows regions of kinetically active sites and presence of percolating back-bone. (c) Instantaneous displacement distributions in presence of steady flow for $\Sigma (= 0.85) > \Sigma_{Y} ( \approx 0.81)$, where $\Sigma_{Y}$ is the yield strength. The solid line shows the respective nearest Gaussian. (d) The corresponding plastic rearrangements are shown by local displacement map, which are non-affine in nature. The data has been obtained for a system of size $N=102400$ in two dimensions using Model 2.
• Figure 3: Dynamic Facilitation in Active Glassy Liquid: (a) Coexistence of slow and fast regions. Spatial maps of particle displacements are shown in arrows. It shows that regions of collective flow and arrested regions coexist together within the same system. Time series of a typical single particle instantaneous displacements in x (b) and y-directions (c) are shown. Associated time series of (d) kinetic energy and (e) potential energy for the specified particle shows the intermittent nature of the dynamics and persistent heterogeneity and occurrence of extreme events in the form of kinetic bursts. The underlying extreme statistics is clearly seen with unusual spikes in the time-series of displacement and kinetic energies, falling on a distribution which is non-Gaussian (data not shown). The data was simulated using Model 3 for a system size $N=100000$ in two dimensions with $f=3$. The system has a threshold for unjamming transition at $f_{C}\approx1.67$ for $N=1000$ as reported in Ref. mandal2020extremedutta2025activity.