Topological order and topological entropy in classical systems

TL;DR

This paper demonstrates that topological order and entropy, originally from quantum physics, also apply to classical systems, providing new insights into their characterization.

Contribution

It introduces a method to construct classical analogs of quantum topological states and explores their potential in understanding classical glassy systems.

Findings

Classical systems can exhibit topological order and entropy.

Half the quantum topological entropy can be retained in classical analogs.

Potential application in characterizing glassy systems.

Abstract

We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure state density matrices to construct corresponding thermally mixed ones that retain precisely half the original topological entropy, a result that we generalize to a whole class of quantum systems. Finally, we suggest that topological order and topological entropy may be useful in characterizing classical glassy systems.