On Principles of Emergent Organization
Adam T. Rupe James P. Crutchfield
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.