Master equation

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.

<math> \frac{dP_k}{dt}=\sum_lT_{kl}P_l <math>

Where P_k is the probability for the system to be in the state k, while the matrix T_kl 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).