Abstract
Complex emergent systems of many interacting components, including complex biological systems, have the potential to perform quantifiable functions. Accordingly, we define "functional information," I(E(x)), as a measure of system complexity. For a given system and function, x (e.g., a folded RNA sequence that binds to GTP), and degree of function, E(x) (e.g., the RNA-GTP binding energy), I(E(x)) = -log(2)[F(E(x))], where F(E(x)) is the fraction of all possible configurations of the system that possess a degree of function > or = E(x). Functional information, which we illustrate with letter sequences, artificial life, and biopolymers, thus represents the probability that an arbitrary configuration of a system will achieve a specific function to a specified degree. In each case we observe evidence for several distinct solutions with different maximum degrees of function, features that lead to steps in plots of information versus degree of function.