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We derive the Hessian geometric structure of nonequilibrium chemical reactionnetworks (CRN) on the flux and force spaces induced by the Legendre duality ofconvex dissipation functions and characterize their dynamics as a generalizedflow. With this structure, we can extend theories of nonequilibrium systemswith quadratic dissipation functions to more general ones with nonquadraticones, which are pivotal for studying chemical reaction networks. By applyinggeneralized notions of orthogonality in Hessian geometry to chemical reactionnetworks, we obtain two generalized decompositions of the entropy productionrate, each of which captures gradient-flow and minimum-dissipation aspects innonequilibrium dynamics.

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions