On Principles of Emergent Organization
This addresses a foundational challenge in physics for researchers, offering a constructive approach to understanding emergent organization, though it appears incremental as it builds on existing mathematical ideas.
The paper tackles the long-standing problem of deriving basic principles for spontaneous self-organization in physics, which has been hindered by mathematical intractability and lack of clear definitions, and proposes a path forward using modern mathematical formulations like intrinsic computation and evolution operators to develop a statistical mechanics for systems far from equilibrium.
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. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.