Stability of perturbed thermodynamic systems

In this note, we consider the problem of studying systems with a thermodynamic structure, i.e., generated by a potential (or a function of a given potential), where the potential contains perturbation components. The objective here is to study how robust thermodynamic-based approaches to study stability of an isolated equilibrium are when the generating potential are not well-known. Generally, through the proposed analysis, it is shown, for a particular class of problems, that general structural properties are preserved under perturbations, in particular the dissipative structure of a particular system identified through homotopy is preserved.