There are a great number of thermodynamic schools, independent of each other, and without a powerful general approach, but with a split on non-equilibrium thermodynamics. In 1912, in relation to the stationary non-equilibrium states, Ehrenfest introduced the fundamental question on the existence of a functional that achieves its extreme value for stable states, as entropy does for the stationary states in equilibrium thermodynamics. Today, the new branch frontiers of science and engineering, from power engineering to environmental sciences, from chaos to complex systems, from life sciences to nanosciences, etc. require a unified approach in order to optimize results and obtain a powerful approach to non-equilibrium thermodynamics and open systems. In this paper, a generalization of the Gouy–Stodola approach is suggested as a possible answer to the Ehrenfest question.