Dynamic Self-Organization Pathways in Complex Systems for the Emergence of Sub-Boundaries, Resilience, Connectivity, and Energy Efficiency

Self-organization is common in complex systems, especially those in a metastable state at critical tipping points. This article examines the concept of energy storage and sub-regions formation during self-organization pathways within a specific region of interest known as the control volume. Spontaneous self-organization typically occurs in response to events that trigger a need to respond to an imbalance in the rate of entropy production within the control volume. All entropy-producing processes generate anti-work, enabling the creation of storable power and new sub-boundary pat-terns. A new concept, called anti-work (and related anti-power), is introduced to explain the stability of sub-regions. Examples of triggers include exceeding a local warming rate, earthquakes, or uniquely shaped bird flight formations aimed at energy efficiency, or supercooling, which is the primary example studied in this article to illustrate self-organization. The main conclusion is that the product of temperature and entropy density rate production remains constant during an entropy-producing process. Self-organization leads to a new order and new sub-boundaries. The resilience of this new order is examined in the context of energy partitioning and sub-boundary formation rates. It is observed that self-organization often follows sigmoidal (S-curve) patterns when selecting process pathways. This feature enables the maximization of entropy generation rate and the corresponding availability anti-power. This seemingly universal mechanism for pathway selection in entropy-producing transformations is closely related to the main findings of this article, namely the maximization of the entropy generation rate coupled with energy storage, which helps establish connections across discrete events.