Clever algorithms for glasses work by time reparametrization

TL;DR

This paper reveals that the slow dynamics of glass-formers can be understood through time reparametrization softness, unifying local mobility constraints and global landscape effects, and explains how modern algorithms exploit this property.

Contribution

It demonstrates that the evolution of glass-formers responds to time reparametrization, reconciling two previously conflicting views and linking algorithm success to reparametrization softness.

Findings

Time reparametrization influences glass dynamics.

Algorithms accelerate relaxation by exploiting reparametrization softness.

Reparametrization softness may apply to broader optimization problems.

Abstract

The ultraslow dynamics of glass-formers has been explained by two views considered as mutually exclusive: one invokes locally hindered mobility, the other rests on the complexity of the configuration space. Here we demonstrate that the evolution responds strongly to the details of the dynamics by changing the speed of time-flow: it has time-reparametrization softness. This finding reconciles both views: while local constraints reparametrize the flow of time, the global landscape determines relationships between different correlations at the same times. We show that modern algorithms developed to accelerate the relaxation to equilibrium act by changing the time reparametrization. Their success thus relies on their ability to exploit reparametrization softness. We conjecture that these results extend beyond the realm of glasses to the optimization of more general constraint satisfaction problems and to broader classes of algorithms.