This paper studies the topological (parameter) entropy of two-parameters systems, as defined by Tsukamoto [39]. We first prove that this entropy is invariant under topological conjugacy and discuss several of its basic dynamical properties. We then compare it with the classical topological entropy of Adler et al. [1] and the extended topological entropy introduced by Cheng [11]. Finally, we define a measure-theoretic parameter entropy via a common invariant measure and establish a variational inequality linking it to the topological (parameter) entropy of two-parameters systems.
