Compatibility of non-ideal equilibrium states with kinetic dynamics

Determine the conditions under which chemical reaction networks with kinetic dynamics given by dx/dt = S j(x) admit stationary states that coincide with the non-ideal equilibrium manifolds V constructed via Legendre duality from strictly convex, non-ideal thermodynamic potentials on the concentration space X (including potentials with quadratic interaction corrections or multicomponent van der Waals-type interactions). Ascertain and characterize the compatibility between these non-ideal equilibrium states and kinetic models, providing criteria that ensure or preclude such compatibility.

Background

The paper develops a Riemannian geometric framework for chemical reaction networks (CRNs), showing that Legendre duality between concentration and potential spaces yields equilibrium manifolds V and that these structures lead to a multivariate Cramer-Rao bound. The authors extend the analysis to non-ideal thermodynamics, including quadratic corrections and multicomponent van der Waals-type interactions, and paper absolute sensitivity as a geometric projection.

While quasi-thermostatic (ideal) CRNs align naturally with kinetic descriptions (e.g., detailed balanced mass-action systems), the paper emphasizes that for non-ideal potentials the geometric construction of equilibrium manifolds V does not automatically guarantee a corresponding kinetic realization. The authors explicitly flag the question of whether, and under what kinetic schemes, such non-ideal equilibrium states can be realized, indicating a gap between thermodynamic geometry and kinetic modeling.