Dynamic Entropy as a Measure of Caging and Persistent Particle Motion in Supercooled Liquids

Abstract

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of dynamical systems and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy $S(\epsilon )$ is defined to equal the inverse of the average first-passage time for a particle to exit a sphere of radius $\epsilon$. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a ``cage'' size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature $T_c$ is approached.

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• De-coupling of Exchange and Persistence Times in Atomistic Models of Glass Formers
• Single Particle Jumps in a Binary Lennard-Jones System Below The Glass Transition
• Fast Dynamics in a Model Metallic Glass-forming Material
• Manifestations of Dynamical Facilitation in Glassy Materials
• Heterogeneous diffusion, viscosity and the Stokes Einstein relation in binary liquids
• Exit-Times and {\Large $\epsilon$}-Entropy for Dynamical Systems, Stochastic Processes, and Turbulence
• Relationship between dynamical heterogeneities and stretched exponential relaxation
• Consequences of Anomalous Diffusion in Disordered Systems Under Cyclic Forcing
• Time Evolution of Entropy in a Growth model: Dependence on the Description
• Thermodynamics and Self-organization of Strongly Coupled Coulomb Clusters: An Experimental Study