Energy and Entropy in Open and Irreversible Chemical Reaction-Diffusion Systems with Asymptotic Stability

This work proposes a novel approach for the study of open systems described by completely irreversible reaction mechanisms in non-homogeneous systems and subject to non-equilibrium boundary conditions. Using the non-equilibrium thermodynamics framework, we consider that in an autonomous system of reaction-diffusion equations, the thermodynamic potentials can be constructed from a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem. By interpreting this Lyapunov function as the free energy and redefining the chemical potentials, we were able to demonstrate the local stability properties of non-equilibrium stationary states, i. e., states that do not change with time due to a complex equilibration of internal and external flows. We demonstrate the consistency of our hypotheses with basic thermodynamic principles such as the spectral decomposition of entropy production and the Glansdorff-Prigogine evolution criterion. We discuss how our approach allows us to understand thermodynamic systems without assuming equilibrium or any kind of reversibility.