Entropy in a category

The Pinsker subgroup of an abelian group with respect to an endomorphism was introduced in the context of algebraic entropy. Motivated by the nice properties and characterizations of the Pinsker subgroup, we generalize its construction in two directions. Indeed, we introduce the concept of entropy function h of an abelian category, and we define the Pinsker radical with respect to h, so that the class of all objects with trivial Pinsker radical is the torsion class of a torsion theory.