Master equation

In physics, chemistry, and related fields, master equations are used to describe the time evolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states.

The name was proposed in 1940:

When the probabilities of the elementary processes are known, one can write down a continuity equation for W, from which all other equations can be derived and which we will call therefore the "master” equation.

— Nordsieck, Lamb, and Uhlenbeck, "On the theory of cosmic-ray showers I: The Furry model and the fluctuation problem" (1940)