Kybernetika 41 no. 2, 143-160, 2005

Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Antonio Di Nola, Anatolij Dvurečenskij, Marek Hyčko and Corrado Manara


We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.