  Power law dynamics is used to describe the stability behavior in metabolic
networks such as chemical reaction networks (CRN's). These systems allow
multiple steady states within a single stoichiometric class. On the other side
thermodynamic constraints such as loop-less fluxes represented by the Gorban
theorem of alternatives applied to these networks reveal considerable
restrictions to their dynamics by eliminating multistability of CRN's in
general. Thermodynamic feasible CRN's are contained in the class of injective
CRN's. We can give an alternative proof of the detailed balance with Brewer's
Fixed Point Theorem. Furthermore we can derive by the loop-less principle the
extended detailed balance. This paper establishes a link between recent
research in CRN theory and thermodynamic basics. The result has also
consequences for the picture of multiple steady states as assumed for cell
differentiation and regulation. CRN's provide from their perspective not enough
means to maintain multistability without regulation or external control.
