Some Properties of Fractal Tsallis Entropy

Abstract

We introduce fractal Tsallis entropy and show that it satisfies Shannon–Khinchin axioms. Analogously to Tsallis divergence (or Tsallis relative entropy, according to some authors), fractal Tsallis divergence is defined and some properties of it are studied. Within this framework, Lesche stability is verified and an example concerning the microcanonical ensemble is given. We generalize the LMC complexity measure (LMC is Lopez-Ruiz, Mancini and Calbert), apply it to a two-level system and define the statistical complexity by using the Euclidean and Wootters’ distance measures in order to analyze it for two-level systems.

Keywords

• fractal Tsallis entropy
• fractal Tsallis divergence
• Lesche stability
• complexity measure
• Wootters’ distance