This paper investigates generalized \(\alpha \) -R-norm entropy within the framework of sequential effect algebras (SEAs). First, the concept of generalized \(\alpha \) -R-norm entropy for partitions on SEAs is introduced and illustrated with examples, emphasizing that it is distinct from Rényi entropy when defined on SEAs. The conditional generalized \(\alpha \) -R-norm entropy on SEAs is defined and examined through appropriate examples. It is shown that the limiting forms of generalized \(\alpha \) -R-norm entropy and conditional generalized \(\alpha \) -R-norm entropy reduce to \(\alpha \) -scaled Shannon-type expressions, while the classical Shannon entropy and conditional Shannon entropy are recovered in the special case \(\alpha = 1\) . Several algebraic and analytical properties of generalized \(\alpha \) -R-norm entropy are also established, yielding several useful characterizations. The paper next introduces generalized \(\alpha \) -R-norm divergence for partitions in SEAs and studies its fundamental properties, demonstrating that the Kullback–Leibler divergence of partitions arises as the limiting case. Finally, using the notion of partitions, generalized \(\alpha \) -R-norm entropy is applied to dynamical systems in SEAs, where it is shown that the associated entropies are invariant under isomorphisms.
