R-norm entropy for partitions of algebraic structures and dynamical systems

In this paper, we define R-norm entropy and conditional R-norm entropy of partitions of algebraic structures, and we establish some of their basic properties. We show that the Shannon entropy and the conditional Shannon entropy of partitions can be derived from the R-norm entropy and the conditional R-norm entropy of partitions, respectively, by letting R tend to 1. Finally, using the notion of entropy for partitions, we define the R-norm entropy of a dynamical system. We prove that the R-norm entropies of isomorphic dynamical systems are equal.