Glassy dynamics in thermally-activated list sorting

TL;DR

This paper demonstrates that a simple thermally-activated list sorting algorithm exhibits glass-like dynamics, including memory and rejuvenation effects, even in small lists, providing insights into glassy behavior.

Contribution

It introduces a minimal model of list sorting that reproduces complex glassy phenomena typically seen in physical glasses.

Findings

Sorting displays memory effects during aging.

Rejuvenation effects are observed in the dynamics.

Glass-like behavior occurs even in small lists.

Abstract

Sorting the integers 1 through $N$ into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally-activated pairwise exchanges of neighboring list elements, we find sorting can display many features of a glass, even for lists as small as $N = 5$. This includes memory and rejuvenation effects during aging --- two hallmarks of glassy dynamics that have been difficult to reproduce in standard glass simulations.