Protected edge currents in stochastic and biological systems

Living and active systems exhibit various emergent dynamics necessary for system regulation, growth, and motility. However, how robust dynamics arises from stochastic components remains unclear. Towards understanding this, we develop topological theories that support robust edge states, effectively reducing the system dynamics to a lower-dimensional subspace. In particular, we will introduce stochastic networks in molecular configuration space that enable different phenomena from a global clock, stochastic growth and shrinkage, to synchronization. These out-of-equilibrium systems further possess uniquely non-Hermitian features such as exceptional points and vorticity. More broadly, our work provides a blueprint for the design and control of novel and robust function in correlated and active systems.