Stability of a class of entropies based on fractional calculus
@article{Ferreira2020StabilityOA, title={Stability of a class of entropies based on fractional calculus}, author={Rui A. C. Ferreira}, journal={Journal of Applied Analysis}, year={2020}, volume={28}, pages={105 - 107} }
Abstract In this work, we argue about the Lesche stability of some systems that are motivated by the use of fractional derivatives.
References
SHOWING 1-8 OF 8 REFERENCES
Instabilities of Rényi entropies
- Computer Science, Physics
- 1982
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
- Mathematics
- 2004
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.
- Computer Science, PhysicsPhysical 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
- Computer Science
- 2009
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.