A state in which the probability distribution of states remains constant over time. This is an important idea in statistical physics, and in Markov chains, where the existence of an equilibrium distribution is not guaranteed. For example, in the simple two-state case with transition matrix i.e. state 1 stays in state 1 with probability 0.25 and moves to state 2 with probability 0.75 while if it is in state 2 it will move to state 1 or stay with probability 0.5. Then statistical equilibrium exists with the probabilities of being in state 1 and state 2 respectively being 0.4 and 0.6.