Self-organization and the Maximum Empower Principle in the Framework of max-plus Algebra

Self-organization is a process where order of a whole system arises out of local interactions between small components of a system. Emergy, defined as the amount of (solar) energy used to make a product or a service, is becoming an important ecological indicator. To explain observed self-organization of systems by emergy the Maximum Empower Principle (MEP) was proposed initially without a mathematical formulation. Emergy analysis is based on four rules called emergy algebra. Most of emergy computations in steady state are in fact approximate results, which rely on linear algebra. In such a context, a mathematical formulation of the MEP has been proposed by Giannantoni (2002). In 2012 Le Corre and the second author of this paper have proposed a rigorous mathematical framework for emergy analysis. They established that the exact computation of emergy is based on the * Corresponding author. Tél.: +33 251 85 83 04 ; fax: +33 251 85 83 49. E-­‐mail address: chams.lahlou@imt-­‐atlantique.fr (C. Lahlou). ar X iv :1 71 2. 05 79 8v 1 [ cs .F L ] 1 6 D ec 2 01 7