On the structure and analysis of complex systems of first-order chemical reactions containing irreversible steps—I general properties

Abstract The mathematical structures of systems of first-order reactions containing some irreversible steps are considerably more complicated than the structures of completely reversible systems because the principle of detailed balancing does not apply to the entire system. Characteristic vectors occur that do not correspond to directly responsible straight line reaction paths and the rate constant matrix cannot always be diagonalised. A decomposition of this system into subsystems of reversible reactions interconnected by irreversible steps allows one to introduce the principle of detailed balancing and leads to the development of theorems that should greatly increase one's ability to study such systems.