Detailed balanced mass action systems
A detailed balanced equilibrium concentration of a mass action system is a point which satisfies
for all . Using the short-hand notation we can rewrite this as for all . A mass-action system is said to be detailed balanced if every equilibrium concentration permitted by the system is a detailed balanced equilibrium concentration.
Detailed balancing guarantees that every elementary step in the reaction mechanism is balanced by a reverse elementary step at equilibrium. Every chemical reaction network which permits a detailed balanced mass action system is reversible (Theorem 2A).
Detailed balancing at equilibrium can be alternatively characterized by the matrix expression
Properties of detailed balanced mass action systems
- Fritz Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Ration. Mech. Anal., 49:172--186, 1972