What is "ergodicity"

n. 1 (context uncountable English) The condition of being ergodic 2 (context countable English) The extent to which something is ergodic

n. an attribute of stochastic systems; generally, a system that tends in probability to a limiting form that is independent of the initial conditions

In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states ( phase space). In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics.

In statistics, the term describes a random process for which the time average of one sequence of events is the same as the ensemble average. In other words, for a Markov chain, as one increases the steps, there exists a positive probability measure at step n that is independent of the probability distribution at initial step 0 (Feller, 1971, p. 271).