Hessian geometric structure of chemical thermodynamic systems with stoichiometric constraints

We establish a Hessian geometric structure in chemical thermodynamics, which describes reaction networks (CRNs) with equilibrium states. In our setup, the ideal gas assumption and mass action kinetics are not required. The existence uniqueness condition of state is derived by using Legendre duality inherent to structure. entropy production during relaxation can be evaluated Bregman divergence. Furthermore, characterized four distinct minimization problems divergence, obtained from generalized Pythagorean theorem originating dual flatness. For case, we confirm that implies Birch's theorem, represented divergence coincides Kullback-Leibler addition, under kinetics, general framework reproduces local detailed balance condition.