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ELEMENTS OF A MATHEMATICAL THEORY OF SUSTAINABLE SYSTEMS
Citation:
Cabezas*, H C. AND B. D. Fath**. ELEMENTS OF A MATHEMATICAL THEORY OF SUSTAINABLE SYSTEMS. Presented at 2000 AIChE Meeting, Los Angeles, CA, 11/12-17/2000.
Description:
The subject of Sustainability has recently attracted enormous interest in the minds of both the public and the scientific and engineering community. The reason for this interest is the fact that the concept of Sustainability holds the promise of a solution to society's long-term environmental problems. Sustainability, however, is a loosely defined concept that has found mathematical definition only in the restricted confines of pollution prevention, economics, ecology, and, perhaps, other disciplines. There is no widely accepted, precise, and testable multidisciplinary definition of Sustainability, and there is no general theory of the subject. This is a problem because without guidance from precise mathematical definitions, a general theory, and testable hypothesis, it is virtually impossible to apply the scientific method to make progress in any area of study. To address this problem a multidisciplinary Sustainability Theory Group has been formed at the US EPA's NRMRL. This paper is based on the work of this group. the objective of this paper is then to briefly discuss some of the work done in the area, to present a definition of Sustainability, and to present the elements of a general theory. The definition and the theory draw heavily on Information Theory and the concept of Fisher Information. Thus, the development of a general Sustainable Systems Theory will be presented along with a criterion based on Fisher Information for system sustainability. The criterion states that Fisher Information decreases over time in unsustainable systems, and that Fisher Information does not decrease over time in sustainable systems. An illlustration of the application of theory and the criterion will be shown using simple Lotka-Volterra prey-predator ecological model. Future directions will be discussed.