Phase transitions mark abrupt changes in system states from "summary" of Complexity by Mitchell M. Waldrop
Phase transitions are pivotal moments in the life of a complex system. These transitions occur when a system suddenly shifts from one state to another, often without warning. Imagine a pot of water simmering on a stove - as the temperature rises, the water undergoes a phase transition from liquid to gas. This shift happens abruptly, transforming the system into a new state. These abrupt changes are not limited to physical systems like water; they also occur in complex systems found in nature, society, and technology. For example, a population of animals may experience a phase transition when food becomes scarce, causing a sudden shift in behavior to adapt to the new conditions. Similarly, a financial market may undergo a phase transition when a bubble bursts, leading to a rapid change in investor behavior. What makes phase transitions so intriguing is their unpredictability. Before a transition occurs, the system may appear stable and unchanging. However, beneath the surface, small fluctuations are building up, even...
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