  We introduce and study a notion of algebraic entropy for self-maps of finite
length of Noetherian local rings, and develop its properties. We show that it
shares the standard properties of topological entropy. For finite self-maps we
explore the connection between the degree of the map and its algebraic entropy,
when the ring is a Cohen-Macaulay domain. As an application of algebraic
entropy, we give a characteristic-free interpretation of the definition of
Hilbert-Kunz multiplicity.
