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International Conference on Complex Systems (ICCS2006)

Exergy Sustainability for Complex Systems

Rush D. Robinett, III
sandia national laboratories

David G. Wilson
sandia national laboratories

Alfred W. Reed
sandia national laboratories

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     Last modified: May 11, 2006

Exergy is the elixir of life. Exergy is that portion of energy available to do work. Elixir is defined as a substance held capable of prolonging life indefinitely, which implies sustainability of life. In terms of mathematics and engineering, exergy sustainability is defined as the continuous compensation of irreversible entropy production in an open system with an impedance and capacity-matched persistent exergy source. Irreversible and non-equilibrium thermodynamic concepts are combined with self-organizing systems theories as well as nonlinear control and stability analyses to explain this definition. In particular, this paper provides a missing link in the analysis of self-organizing systems: a tie between irreversible thermodynamics and Hamiltonian systems. As a result of this work, the concept of ``on the edge of chaos" is formulated as a set of necessary and sufficient conditions for stability and performance of sustainable systems.

In this paper simplified models are developed and utilized to address the notion of sustainability of a lifestyle. The purpose of this paper is to present the concept of exergy sustainability based on irreversible and non-equilibrium thermodynamics combined with some concepts from self-organization and adaptivity as well as nonlinear stability and control. The result of this synthesis is the mathematical definition of sustainability based on a fundamental driver and input, exergy rate, to a self-organizing system. In fact, exergy rate (power) input, is a single point failure. The flow of exergy into an open system that is continuously undergoing self-organization and adaptivity determines whether the system will persist or disintegrate. As a result, the balance of exergy flows into and out of the system versus the exergy consumption, irreversible entropy production, in the system will be studied.

Traditionally, exergy concepts are founded in the first and second laws of thermodynamics in the field of physics. However, these laws have both economical and environmental significance as well and can be applied in a more universal manner. Assessment of economic factors, that are based on the second law of thermodynamics are: i) exergy is not conserved and ii) exergy can be used as a common measure of resource quality along with quantity (i.e., materials and energy) [1]. Exergy from a physics standpoint is formally defined as the maximum amount of work that a subsystem can do on its surroundings as it approaches thermodynamic equilibrium reversibly or the degree of distinguishability of a subsystem from its surroundings [1]. Therefore, exergy can be used to measure and compare resource inputs and outputs which include wastes and losses [1]. For economic processes exergy is consumed not conserved. In addition, exergy can be used as a measure of assessing technical progress for economic growth theory. In this paper these concepts with be developed with several clarifying examples.

[1] R.U. Ayres, Eco-thermodynamics: Economics and the Second Law, Ecological Economics, 26, 1998, pp. 189-209.

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