On principles of emergent organization

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization—intrinsic computation and evolution operators—lays out a way to overcome these challenges. Additionally, we show how intrinsic computation and evolution operators combine to produce a general framework showing physical consistency between emergent behaviors and their underlying physics. This statistical mechanics of emergence provides a theoretical foundation for data-driven approaches to organization necessitated by analytic intractability. Taken all together, the result is a constructive path towards principles of organization that builds on the mathematical identification of structure.