Entropy of automorphisms in algebra (groups, rings).
Justin Peters introduced a way to define entropy for automorphisms of discrete abelian groups in "Entropy on discrete abelian groups", Advances in Math. 33, No.1 (1979), 1-13. This notion is dual to the Kolmorgorov-Sinai entropy for the dual automorphism on the compact abelian dual group. There have been many papers since exploring this idea.