In this chapter review measures of emergence, self-organization, complexity, homeostasis, and autopoiesis based on information theory. These measures are derived from proposed axioms and tested in two case studies: random Boolean networks and an Arctic lake ecosystem. Emergence is defined as the information produced by a system or process. Self-organization is defined as the opposite of emergence, while complexity is defined as the balance between emergence and self-organization. Homeostasis reflects the stability of a system. Autopoiesis is defined as the ratio between the complexity of a system and the complexity of its environment. The proposed measures can be applied at multiple scales, which can be studied with multi-scale profiles.
The generality and usefulness of the proposed measures will be evaluated gradually, as these are applied to different systems. These can be abstract, machines, biological (ecosystems, organisms), economic, social or technological. The potential benefits of general measures as the ones proposed here are manifold. Even if with time more appropriate measures are found, aiming at the goal of finding general measures which can characterize complexity, emergence, self-organization, homeostasis, autopoiesis, and related concepts for any observable system is a necessary step to take.