Modeling and Predicting Self-Organization in Dynamic Systems Out of Thermodynamic Equilibrium; Part 1

Self-organization in complex systems is a process in which internal entropy is reduced and emergent structures appear that allow the system to function in a more competitive way with other states of the system or with other systems. It occurs only in the presence of energy gradients, facilitating energy transmission through the system and entropy production. Being a dynamic process, self-organization requires a dynamic measure and dynamic principles. The principles of decreasing unit action and increasing total action and the principle of decreasing unit entropy and increasing total entropy are dynamic variational principles that are viable to utilize in a self-organizing system. Based on this, average action efficiency can serve as a quantitative measure of the degree of self-organization. Positive feedback loops connect this measure with all other characteristics of a complex system, providing all of them with a mechanism for exponential growth, and indicating power law relationships between each of them as confirmed by data and simulations. In this study, we apply those principles and the model to agent-based simulations of ants traveling between two locations on a 2D grid. We find that those principles explain self-organization well and that the results confirm the model. We derive a compact model of ant-behavior based on the action of their trajectories, and then estimate a variety of metrics from the simulated behavior. By measuring action efficiency we can have a new answer to the question: "What is complexity and how complex is a system?". This work shows the explanatory and predictive power of those models, which can help understand and design better complex systems.