  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. We introduce the concept of entropy function h
of an abelian category and 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.
