Before revision:  From a theoretical viewpoint it states that the exclusion (presence) of closed reactions loops makes possible (impossible) the definition of a thermodynamic potential and vice versa.
After revision:  From a theoretical viewpoint it is equivalent to the Clausius formulation of the second law for the out of equilibrium steady states of chemical networks, i.e. it states that the exclusion (presence) of closed reactions loops makes possible (impossible) the definition of a thermodynamic potential and vice versa.