Differential Bases of Emergy Algebra

The well-known rules of Emergy Algebra, originally formulated in steady state conditions, are reconsidered and analyzed from a dynamic point of view. In such a sense the paper points out their corresponding differential bases. The latter, in turn, represent the preferential guide to recognize their most profound physical meaning. However, for the sake of completeness, a possible generalization of the same rules from steady state to variable conditions is also considered. The analysis is particularly focused on the three fundamental generative processes represented by co-production, inter-action, and feed-back, which are formally described (under dynamic conditions) by means of the Incipient Fractional Differential Calculus. In so doing, the mathematical method adopted succeeds in defining the output exceeding Quality of the mentioned processes by means of the corresponding Ordinality of their associated output Transformities. Such a dynamic analysis enables us to show that the rules of Emergy Algebra proposed by Prof. Odum under steady state conditions have a well-founded dynamic physical nature, adequately described by the differential operators adopted. The analysis also shows that the originally conceived rules of Emergy Algebra continue to hold even when the dynamics of a process becomes extremely complicated.