Master equation

Summary

A master equation is a system of linear differential equations for probabilities $P_t(x)$. Here $P_t(x)$ is the probability that a system is in the state $x$ at time $t$. It balances the flow of probability into each state against the flow out of it, using the transition rates between states. It is the forward equation of a continuous-time Markov chain, written in the form used in physics and chemistry. Master equations model chemical reactions, population dynamics, queues and stochastic lattice dynamics.