Journal of Mathematical Chemistry

, Volume 54, Issue 2, pp 503–526 | Cite as

Entropy of chemical processes versus numerical representability of orderings

  • M. J. Campión
  • G. Arzamendi
  • L. M. Gandía
  • E. Induráin
Original Paper


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 Carathéodory, 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.


Entropy Carathéodory axioms Numerical representability of orderings Intransitive processes Interval orders Semigroups 

Mathematics Subject Classification

80A05 (Primary) 80A10 06A06 06F30 26A48 54F05 91B16 92E20 



Thanks are given to the editor and three anonymous referees for their valuable suggestions and comments on a previous version of the manuscript.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • M. J. Campión
    • 1
  • G. Arzamendi
    • 2
  • L. M. Gandía
    • 2
  • E. Induráin
    • 1
  1. 1.Department of Mathematics and Institute for Advanced Materials (InaMat)Public University of NavarrePamplonaSpain
  2. 2.Department of Applied Chemistry and Institute for Advanced Materials (InaMat)Public University of NavarrePamplonaSpain

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