Thermodynamics can be contrived in many different but equivalent guises. For instance, in the entropy formulation, the equilibrium states are characterized by the maximum of the entropy as a function of extensive parameters, subject to the constraints in place, such as that of constant internal energy. The corresponding theoretical framework is equivalent to the energy formulation, in which the equilibrium states have minimum energy, and the entropy is constant. In both cases, as well as in any other equivalent formulation of thermodynamics, an equilibrium state is characterized by the extremum of a fundamental quantity, under a given set of constraints.