Phase transitions are points at which a system's behavior changes abruptly due to a particularly abrupt change in the underlying parameters that define its behavior. This is most prominently observed in physical systems, such as a liquid in equilibrium undergoing a phase transition when the temperature is increased, resulting in the liquid heating into a gas. However, this concept also extends to other systems, such as biological systems exhibiting a shift in behavior when a particular internal or external parameter, such as nutrient availability or temperature, changes in a particular way. In this way, phase transitions are useful in understanding and manipulating the behavior of complicated systems.

See also: feedback loop, complex system, possibility space, game theory, hill climbing