Entropy of chemical processes versus numerical representability of orderings

Leaning on the mathematical concept of an interval order, we show that intransitivities that appear in several chemical processes, mainly related to mixing and competition, can actually be located and handled within a thermodynamical setting whose basis is the classical axiomatics due to Caratheodory, now using two intertwined entropy functions. Interdisciplinary comparisons to other similar theories (e.g., Utility Theory) are also made, pointing out the common mathematical background based on the numerical representability of total preorders and interval orders.