Any change that takes place in the phase of one quantity or in the relative phase. If the change is characterized by an abrupt jump in the value of the order parameter, then it is a first-order transition. If the change evolves smoothly to or from a zero value, it is a continuous phase transition (e.g., the onset of ferromagnetism when iron is cooled below the Curie temperature of 1043K). When the change is not only abrupt, but also accompanied by events such as fluctuations and breakdowns in correlations between dimensions of an order parameter, then it constitutes a second-order transition. If accompanied by other events (e.g., hysteresis), this can be evidence for a discontinuous (non-equilibrium) phase transition that involves non-linear qualitative change in the dynamics of the order parameter. J.A.Scott Kelso among others, has demonstrated the existence of such transitions in changes in human movement coordination (viz., a sudden shift from anti-phase to in-phase at the order parameter level, when the movement frequency that is the control parameter attains a critical value).
See Bifurcation, Catastrophe theory, Control parameter, Hysteresis, Order parameter, Quantitative and qualitative change, Phase, Synergetics, Transition