Some consequences of thermodynamic feasibility for the multistability   and injectivity in chemical reaction networks
  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. 
Gunther Friedrich Neumann
math.DS