Kinetic derivation of the Hessian geometric structure in chemical reaction networks

The theory of chemical kinetics forms the basis to describe dynamics reaction networks. Owing physical and thermodynamic constraints, networks possess various structures, which can be utilized characterize important properties In this work, we reveal Hessian geometry underlies demonstrate how it originates from interplay stoichiometric constraints. Our derivation is based on kinetics, assume law mass action equilibrium states by detailed balance condition. obtained geometric structure then related thermodynamics via appearing in a pure derivation. We demonstrate, fact that both complex balanced form toric varieties, framework extended nonequilibrium steady states. conclude provides natural capture aspects