On Local Tsallis Entropy of Relative Dynamical Systems

In this contribution, we introduce the concepts of local Tsallis entropy and local Tsallis conditional entropy of partitions in the relative probability measure space, and derive the basic properties of the suggested measures. In particular, subadditivity property for local Tsallis entropy of partitions is established. Subsequently, by means of the suggested notion of local Tsallis entropy of a partition, we define the local Tsallis entropy of a relative dynamical system. Some properties concerning this measure are proved. Finally, it is shown that the local Tsallis entropy of relative dynamical systems is invariant under isomorphism of relative dynamical systems.