ABSTRACT
Critical transitions, or large changes in the state of a system after a small change in the system’s external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics. The collapse of socioecological systems, such as the historical collapse of societies and civilizations, can be precipitated by such a critical transition. Statistical physics first confronted the problem of emergent phenomena such as critical transitions in the late 1800s and early 1900s, culminating in the theory of phase transitions. However, although phase transitions show a strong resemblance to critical transitions, the theoretical connections between the two sets of phenomena are tenuous at best, and it would be advantageous to make these theoretical connections more concrete in order to take advantage of the theoretical methods developed by physicists to study phase transitions. Here we attempt to explicitly connect the theory of critical transitions in complex systems to phase transitions in physics. We initially find something paradoxical, that while many critical transitions closely resemble discontinuous/first-order phase transitions, many of the early warning indicators developed to anticipate critical transitions, such as critical slowing down or increasing spatial correlations, occur instead in continuous/second-order phase transitions. We attempt to reconcile these disparities by making the connection with other phenomena associated with discontinuous phase transitions, such as spinodal instabilities and metastable states.
