Foundations of Chemical Reaction Network Theory pp 321-358 | Cite as

# Deficiency Zero Theory Foundations and Some Key Propositions

## Abstract

At the end of this chapter, we will complete the proofs of the Deficiency Zero Theorem and some of its variants. A considerable amount of the work has already been done: In Chapter 13 we described the dynamical consequences that accrue to a kinetic system having the quasi-thermodynamic property. In Chapter 15, we indicated how, for a mass action system, complex balancing at a positive equilibrium ensures quasi-thermodynamicity. In this chapter we will, among other things, connect complex balancing in a kinetic system to architectural properties of the underlying reaction network—in particular to the network’s deficiency and to its graphical structure. The Deficiency Zero Theorem derives from these connections.

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