Unveiling classes of self-organization across complex multiscale stochastic systems through a generalized theory of interactions*

Complex multiscale stochastic systems (CMSS), are systems composed of many objects and processes that interact with each other in non-trivial manners (i.e. interdependent), whose structure and behavior can be described at several nested, coupled scales by different principles and laws. Yet, these remain causally connected and their spatio-temporal evolution and interactions are inherently stochastic, leading to complementarity relations with non-zero statistical uncertainty. CMSS show overall consistency with fundamental physical laws such as conservation of energy and irreversible thermodynamics. Understanding the principles behind self-organization across these systems constitutes a major milestone toward addressing grand challenges in science and society.

We present here the application of a generalized theory of interactions (GToI) to the problem of characterizing self-organization across CMSS instances. We describe the formulation of the GToI events in a space whose structure is described by information geometry, the interaction space of the system, which contains information about classes of interactions, their relations and their evolution under various transformations; the theory, by construction, is an ensemble theory. We describe how core aspects of the GToI map onto hallmarks of self-organization across various physical systems. Finally, we construct a classification describing modes of self-organization across these systems, and provide their general construction by defining archetypal transition paths between interaction spaces. Our work suggests that the GToI can capture essential features of self-organization across systems that exhibit higher order interactions, which then can be used to derive system-specific computation schemes.