Stability of a class of entropies based on fractional calculus

  title={Stability of a class of entropies based on fractional calculus},
  author={Rui A. C. Ferreira},
  journal={Journal of Applied Analysis},
  pages={105 - 107}
  • R. Ferreira
  • Published 5 November 2020
  • Mathematics, Computer Science
  • Journal of Applied Analysis
Abstract In this work, we argue about the Lesche stability of some systems that are motivated by the use of fractional derivatives. 



Entropies based on fractional calculus

Instabilities of Rényi entropies

We show that for systems with a large number of microstates Rényi entropies do not represent experimentally observable quantities except the Rényi entropy that coincides with the Shannon entropy.

Stabilities of generalized entropies

The generalized entropic measure, which is maximized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

  • S. Abe
  • Computer Science, Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

Ubriaco, Entropies based on fractional calculus

  • Phys. Lett. A
  • 2009

On the stability of generalized entropies

Several sharp inequalities concerning the uniform continuity of some generalized entropies are derived by the use of a probabilistic coupling technique and generalizing a recent result of Zhang.

We note that, for λ > 0, the function f σ,λ (x) is differentiable at x = 1. Therefore, if we define by f −1 (x) = d dx x [(λ − ln(x)) σ − λ σ