  In this paper, we define the core entropy for postcritically-finite Newton
maps and study its continuity within this family. We show that the entropy
function is not continuous in this family, which is different from the
polynomial case studied by Thurston, Gao, Dudko- Schleicher, Tiozzo [Th+, GT,
DS, Ti2], and describe completely the continuity of the entropy function at
generic parameters.
