Applications
Network analogs have been constructed for a wide variety of physical systems, and have proven extremely useful in analyzing their dynamic behavior. The classical application area for network theory and Tellegen's theorem is electrical circuit theory. It is mainly in use to design filters in signal processing applications.
A more recent application of Tellegen's theorem is in the area of chemical and biological processes. The assumptions for electrical circuits (Kirchhoff laws) are generalized for dynamic systems obeying the laws of irreversible thermodynamics. Topology and structure of reaction networks (reaction mechanisms, metabolic networks) can be analyzed using the Tellegen theorem.
Another application of Tellegen's theorem is to determine stability and optimality of complex process systems such as chemical plants or oil production systems. The Tellegen theorem can be formulated for process systems using process nodes, terminals, flow connections and allowing sinks and sources for production or destruction of extensive quantities.
A formulation for Tellegen's theorem of process systems:
where are the production terms, are the terminal connections, and are the dynamic storage terms for the extensive variables.
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