  In the framework of irreversible thermodynamics, we study autonomous systems
of reaction-diffusion equations to show how the entropy and free energy of an
open and irreversible reactor depend on concentrations. To do this, we find a
Lyapunov function that depends directly on the eigenvalues and eigenvectors of
the linearized problem valid for linear and asymptotically stable systems. By
suggesting the role of this Lyapunov function as internal free energy, we were
able to reflect the properties of the dynamical system directly into the second
law of thermodynamics making a redefinition of the chemical potentials. We
demonstrate the consistency of our hypotheses with basic thermodynamic
principles such as the proportionality between flows and forces proposed by
Onsager, the spectral decomposition of entropy production and the
Glansdorff-Prigogine evolution criterion of a thermodynamic system.
