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.

For the master equation used in quantum physics, see Lindblad equation. For the classical and quantum master equations in quantum field theory, see Batalin–Vilkovisky formalism. For the master equation analyzed in algorithmic complexity, see Master theorem (analysis of algorithms).

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.

— On the theory of cosmic-ray showers I the furry model and the fluctuation problem (1940)
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