In a biological context, self-maintenance means that simple chemical inputs are transformed through metabolic cycles into all those molecules that an organism needs to persist. Framed this way the term organization describes more than just a set of molecules, it refers also to a network of functional relationships that allows the persistence of an organism in spite of the fact that every single molecule may be continuously replaced. Common features of such systems include resistance to perturbation, extensibility, and history dependence. It is curious, given the importance of this topic, that there exists no scientific tradition in the formal study of self-maintenance. We claim that only two abstractions from chemistry are essential.
First chemistry is constructive , i.e., the collision of molecules can generate new molecules.
Second there exist equivalence classes such that many different reactions can produce the same stable products. We chose -calculus as a formal system because it captures these two abstractions, constructivism and equivalence relations and nothing more. We call this a constructive dynamical system . In a conventional dynamical system all components and all interactions are given explicitly at the outset and the mathematical apparatus is used to compute, for example, equilibrium distributions of the components of the system. In contrast, the components of biological and chemical systems endogenously construct new components upon interaction.