Deficiency Zero Theory Foundations and Some Key Propositions

  • Martin Feinberg
Part of the Applied Mathematical Sciences book series (AMS, volume 202)


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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Authors and Affiliations

  • Martin Feinberg
    • 1
  1. 1.Chemical & Biomolecular Engineering, The Ohio State UniversityColumbusUSA

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