# Topological localization in out-of-equilibrium dissipative systems

## TL;DR

This paper demonstrates that topological protection concepts can be applied to out-of-equilibrium dissipative systems, including stochastic networks and driven particle collections, with implications for biological and synthetic systems.

## Contribution

It extends topological protection notions from electronic and mechanical systems to far-from-equilibrium dissipative processes, showing their general applicability.

## Key findings

- Topological protection applies to driven, dissipative systems.
- Dissipative couplings breaking time reversal symmetry are crucial.
- Boundary modes exhibit topological robustness in out-of-equilibrium systems.

## Abstract

In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of principle that notions of topological protection, established in the context of electronic and mechanical systems, do indeed extend generically to processes that operate out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.