Topology protects chiral edge currents in stochastic systems

TL;DR

This paper introduces topologically protected chiral edge currents in stochastic networks, demonstrating their robustness and potential for controlling long-timescale dynamics in complex systems.

Contribution

It presents a novel topological framework for stochastic systems with emergent edge currents, linking non-Hermitian physics to robust dynamical behavior.

Findings

Edge currents arise in topological phase due to bulk-boundary correspondence.

Edge currents are robust to defects and blockages.

Tuning parameters enables diverse dynamical phenomena such as synchronization.

Abstract

Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase due to the bulk-boundary correspondence and dominate the system dynamics in the steady-state, further proving robust to defects or blockages. We demonstrate the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity, while characterizing the edge state localization. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, dynamical growth and shrinkage, and synchronization. Our construction provides a novel topological formalism for stochastic systems and fresh insights into non-Hermitian physics, paving the way for the prediction of robust dynamical states in new classical and quantum platforms.