A master equation is a phenomonological first order differential equation describing the time-evolution of the probability of a system to occupy each one of a discrete set of states.
Where Pk is the probability for the system to be in the state k, while the matrix Tkl is filled with constants.
Many physical problems in classical, quantum mechanics and problems in other sciences, can be reduced to the form of a master equation, thereby performing a great simplification of the problem (see mathematical model).