Entropy Rate

The long-run average Shannon information produced per symbol by a stochastic process, typically defined as the limit H = lim_{n→∞} (1/n) H(X1,...,Xn) or equivalently H = lim_{n→∞} H(Xn | X1,...,Xn−1) when the limit exists.

Asymptotic average Shannon information per produced symbol of a stochastic language source: formally the limit of the conditional entropy per symbol H(X_n | X_{n-1}, X_{n-2}, ...) for a stationary stochastic process or, more generally, the per‑symbol expected information under the specified source model and sampling regime.