Identifying non-ideal reaction-diffusion systems unable to maintain diffusion out-of-equilibrium

We develop a general method, based on the construction of a kinetic potential serving as a Lyapunov function, to establish when diffusion necessarily equilibrates in non-ideal reaction-diffusion systems under arbitrary driving by autonomous homogeneous chemostats. This equilibration of diffusion implies vanishing diffusion currents and homogeneous chemical potentials, while reactions can remain far from equilibrium. Using this method, we generalize the results of Avanzini et al., J. Chem. Phys. 161, 174108 (2024), by relaxing some of the underlying assumptions. Specifically, we show that diffusion equilibrates in reaction-diffusion systems whose chemical reaction network is either pseudo-detailed balanced, with reaction fluxes controlled by the stoichiometry of reactants and products, or complex balanced, with reaction fluxes controlled only by the stoichiometry of the reactants. These different constraints on the reaction fluxes are shown to originate from the distinct stoichiometric properties of the two classes of networks.