# Dynamic facilitation theory: A statistical mechanics approach to dynamic arrest

## TL;DR

This paper reviews dynamic facilitation theory as a statistical mechanics approach to understanding the dynamic arrest in supercooled liquids, emphasizing the role of excitations and hierarchical motion without requiring a growing static correlation length.

## Contribution

It provides a minimal statistical mechanics framework for dynamic facilitation, clarifying its differences from other theories and deriving the parabolic law for relaxation time.

## Key findings

- Dynamic arrest can occur without a growing static length scale.
- The parabolic law describes the structural relaxation time.
- Dynamic facilitation scenarios are compatible with claims of static length growth.

## Abstract

The modeling of supercooled liquids approaching dynamic arrest has a long tradition, which is documented through a plethora of competing theoretical approaches. Here, we review the modeling of supercooled liquids in terms of dynamic "defects", also called excitations or soft spots, that are able to sustain motion. To this end, we consider a minimal statistical mechanics description in terms of active regions with the order parameter related to their typical size. This is the basis for both Adam-Gibbs and dynamical facilitation theory, which differ in their relaxation mechanism as the liquid is cooled: collective motion of more and more particles vs. concerted hierarchical motion over larger and larger length scales. For the latter, dynamic arrest is possible without a growing static correlation length, and we sketch the derivation of a key result: the parabolic law for the structural relaxation time. We critically discuss claims in favor of a growing static length and argue that the resulting scenarios for pinning and dielectric relaxation are in fact compatible with dynamic facilitation.