Variational approach to chemical reactions beyond local equilibrium

The formal description of chemical reactions far from equilibrium is an open task. Chemical reactions are central to various phenomena in life, industry, and the environment. In this work, we use a variational principle within the framework of extended irreversible thermodynamics to obtain relaxation equations for the fast variables and close the balance equations. Our approach extends traditional local equilibrium thermodynamics by incorporating formal expressions for the unknown generalized equations of state, which we can expand in low and higher-order terms, allowing for a more comprehensive representation of non-linear and dissipative phenomena and capturing wave-like behaviours relevant to oscillatory chemical systems. The formalism aligns well with previous theoretical works and provides additional insights into the influence of diffusion fluxes on reaction rates. The resulting equations may describe velocity reactions with different relaxation times and diffusion reactions. We present a comparison of our results with experiments in the context of a particular chemical kinetics case. We emphasize the need for practical applications in areas like environmentally friendly chemical reaction systems.