Topological building blocks of nonequilibrium response

Nonequilibrium systems can exploit energy to amplify their sensitivity to external stimuli, allowing them to be harnessed for a variety of functions in both engineered devices and living organisms. An assortment of theoretical results capture different facets of this nonequilibrium amplification, including fluctuation-response relations as well as bounds and constraints that limit the potential behavior. Here, we take a broader perspective, aiming for a systematic characterization of the full range of possible response behaviors. For a wide class of nonequilibrium dynamics, we identify a collection of optimally sensitive models whose behavior is determined by the topology of the state space. We further conjecture that every response can be written as a convex combination of these optimal models, thereby structuring the entire space of responses. We use this geometric perspective to put sensitivity limits on nonmonotonic biochemical input-output functions, and identify all optimal kinetic schemes for the unordered binding of molecules among three sites.