Geometry of Nonequilibrium Reaction Networks

Explore the geometric foundations of nonequilibrium reaction networks in this 58-minute lecture by Vivien Lecomte at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the extension of Hill and Schnakenberg's theory for Markov processes and linear biochemical networks to arbitrary chemical reaction networks. Discover how hypergraphs represent many-to-many reactions and learn about new procedures for building bases of cycles and cocycles. Examine the interpretation of these concepts in terms of circulations and gradients, and understand their role in projecting nonequilibrium observables onto relevant subspaces. Investigate the theory's application to non-equilibrium reaction networks with mass-action kinetics, enriched by insights from stochastic models. Gain insights from joint work with Sara Dal Cengio and Matteo Polettini, referencing arXiv:2208.01290 [cond-mat.stat-mech].