Emergy Analysis as the First Ordinal Theory of Complex Systems

The linguistic-mathematical tools developed to give an appropriate mathematical formulation to the Maximum Em-Power Principle, together with the already shown validity of the Rules of Emergy Algebra under variable conditions, suggested a possible development of a General Ordinal Theory of Complex Systems. This can ideally be thought of as an appropriate “transposition” of theorems and concepts of the well-known “Systems Theory” (conceived in terms of traditional Differential Calculus) into a new Mathematical Theory of Ordinal Systems, where the latter are described and analyzed in terms of “Incipient” Differential Calculus. The activity aimed at formally defining some basic concepts (such as “Ordinality”, “Information”, “Organization”, etc.) led us to recognize an unexpected “similarity” between the concept of “Information” adopted and Odum’s Transformity. Further consequential developments of such an initial analogy led us to the conclusion that Emergy Analysis can be considered as being the First Ordinal Theory in the field of Thermodynamics of self-organizing Systems. This result definitely becomes evident when the basic cardinal quantities, which in Emergy Analysis are understood in an “ordinal sense”, assume their explicit and appropriate formal expressions corresponding to their Ordinal nature. In particular, in such a context the Rules of Emergy Algebra can adherently be seen as specific Rules of “genesis and transfer of Ordinality”, when the latter is accounted for in terms of its associated “Ordinal Information”.