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, I develop topological theories that support robust edge currents, effectively reducing the system dynamics to a lower-dimensional subspace. In particular, I will introduce stochastic networks in molecular configuration space that can model different systems from a circadian clock to the stochastic dynamics of cytoskeletal filaments. The edge localization results in new properties, e.g., the clock demonstrates increased precision with simultaneously decreased cost. These out-of-equilibrium systems further possess uniquely non-Hermitian features such as exceptional points and vorticity. More broadly, my work provides a blueprint for the design and control of novel and robust function in correlated and active systems.

https://baylor.zoom.us/j/88302943728?pwd=Zm92Mk1EYUxLUWl5d2cxZmM4SC94Zz09