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

TL;DR

This paper mathematically formulates the Maximum Empower Principle using max-plus algebra, demonstrating its connection to combinatorial optimization and ecological self-organization.

Contribution

It introduces a max-plus algebra framework for the MEP, providing a rigorous mathematical basis and linking ecological theory with dynamic systems.

Findings

Empower computation is equivalent to a combinatorial optimization problem.

The axiomatic basis defines emergy as a recursive max-plus linear function.

The paper proves the MEP within this mathematical framework.

Abstract

Self-organization is a process where order of a whole system arises out of local interactions between small components of a system. Emergy, spelled with an 'm', defined as the amount of (solar) energy used to make a product or service, is becoming an important ecological indicator. The Maximum Empower Principle (MEP) was proposed as the fourth law of thermodynamics by the ecologist Odum in the 90's to explain observed self-organization of energy driven systems. But this principle suffers a lack of mathematical formulation due to an insufficiency of details about the underlying computation of empower (i.e. emergy per time). For empower computation in steady-state an axiomatic basis has been developed recently by Le Corre and the second author of this paper. In this axiomatic basis emergy is defined as a recursive max-plus linear function. Using this axiomatic basis and a correspondance between ecological theory and dynamic systems theory, we prove the MEP. In particular, we show that the empower computation in steady-state is equivalent to a combinatorial optimization problem.