Glasses and aging: A Statistical Mechanics Perspective

Abstract

CONTENTS I. Glossary 1 II. Definition of the subject 2 III. Phenomenology 3 A. Basic facts 3 B. Static and dynamic correlation functions 5 References 42 I. GLOSSARYWe start with a few concise definitions of the most important concepts discussed in this article.Glass transition-For molecular liquids, the glass transition denotes a crossover from a viscous liquid to an amorphous solid. Experimentally, the crossover takes place at the glass temperature, T g , conventionally defined as the temperature where the liquid's viscosity reaches the arbitrary value of 10 12 Pa.s. The glass transition

Graph-combinatorial approach for large deviations of Markov chains

“…Furthermore, once we fix the state-space connectivity and probability weights, it would be interesting to understand the interplay between the long-time limit and the large number of states limit. In the framework of Markov chains satisfying detailed balance, this approach could, in principle, be adopted to investigate transient behaviour and metastability in rough energy landscapes, a problem relevant to many areas in statistical physics [41,42]. More generally, Markov chains that satisfy global balance but not detailed balance are a paradigmatic model for out of equilibrium phenomena.…”

“…In ( 40) each term has a clear physical interpretation: λ 1 , in (41), is the geometric -viz. related to the connectivity of the graph G -entropy of a random walk on a graph with nodes and links contributions, akin to the entropy of a free particle; λ 2 , in (42), is the entropy due to the dynamics, encoded in the transition matrix; λ 3 , in ( 43), is the tilting potential necessary to drive the system towards a fluctuation of the pair empirical occupation measure; finally, λ 4 in ( 44), enforces the normalisation and Kirchhoff-law (global balance). We can calculate the leading order in n of (39) via a saddle-point approximation, arriving at…”

Emergence of two-level systems in glass formers: a kinetic Monte Carlo study

“…Most liquids can be quenched into the glassy state by undergoing a glass transition, a phenomenon actively studied for decades [1,2]. When further cooled below ∼1K, it was found by Zeller and Pohl that the heat capacity of glasses is proportional to the temperature T , well exceeding Debye's T 3 relation based on acoustic phonons [3].…”

“…Therefore, TLS is likely an intrinsic component in glasses and should be relevant to the glass transition and glassy dynamics in general. Yet, TLS at present plays little role in major theories of glass transition [1,2]. Concerning particle simulations, both molecular dynamics (MD) simulations [13] and lattice models [14] can reproduce many features of glasses.…”

Predicting nonlinear physical aging of glasses from equilibrium relaxation via the material time

“…Describing and predicting physical aging has been a focus of glass science for many years, yet the subject still presents challenges [10,20]. We here address the fundamental concept of a material ("reduced") time controlling aging, which was proposed by Narayanaswamy in 1971 in a paper dealing with the physical aging of oxide glasses [6].…”