Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions

We derive the Hessian geometric structure of nonequilibrium chemical reaction networks on flux and force spaces induced by Legendre duality convex dissipation functions characterize their dynamics as a generalized flow. With this structure, we can extend theories systems with quadratic to more general cases nonquadratic ones, which are pivotal for studying networks. By applying notions orthogonality in geometry networks, two decompositions entropy production rate obtained, each captures gradient-flow minimum-dissipation aspects dynamics.