Entropy

Round 1

Reviewer 1 Report

The concept of the  phi entropy and also other entropies like exponential entropy are needed to discuss in this paper.

Some references and related papers such as below may be useful.

Chafaï, D. (2004). Entropies, convexity, and functional inequalities, On $\Phi $-entropies and $\Phi $-Sobolev inequalities. Journal of Mathematics of Kyoto University, 44(2), 325-363.

Chafaï, D. (2004). Entropies, convexity, and functional inequalities, On $\Phi $-entropies and $\Phi $-Sobolev inequalities. Journal of Mathematics of Kyoto University, 44(2), 325-363.

Nguyen, V. H. (2018). $\Phi-$ entropy inequalities and asymmetric covariance estimates for convex measures. arXiv preprint arXiv:1810.07141.

Dolbeault, J., & Li, X. (2018). φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations. Mathematical Models and Methods in Applied Sciences, 28(13), 2637-2666.

Menéndez, M. L., Morales, D., Pardo, L., & Salicrú, M. (1997). (h, Φ)-entropy differential metric. Applications of Mathematics, 42(2), 81-98.

Valero-Toranzo, I., Zozor, S., & Brossier, J. M. (2017). Generalization of the de Bruijn Identity to General $\phi $-Entropies and $\phi $-Fisher Informations. IEEE Transactions on Information Theory, 64(10), 6743-6758.

Pal, N. R., & Pal, S. K. (1992). Some properties of the exponential entropy. Information sciences, 66(1-2), 119-137.

Abbasnejad, M., Arghami, N. R., Morgenthaler, S., & Borzadaran, G. M. (2010). On the dynamic survival entropy. Statistics & probability letters, 80(23-24), 1962-1971.

Panjehkeh, S. M., Borzadaran, G. R. M., & Amini, M. (2017). Results related to exponential entropy. International Journal of Information and Coding Theory, 4(4), 258-275.

Entropy estimation and entropy in reliability (past+residual) entropy can also mention in this work.

Author Response

I am grateful to Referee 1 for his/her suggestion of including, within the Entry, the Phi-entropy and the Pal and Pal exponential entropy, and providing two corresponding groups of references. We have selected one reference from each group of references. It is not possible to include more that this, given the fact that there are more than 50 different entropic functionals in the literature, and that it is mandatory to preserve some equilibrium among all those. The corrections are in  RED in the revised manuscript.

Reviewer 2 Report

The paper provides a broad discussion of the notion of entropy and its applications. After briefly recounting the history of the concept, Boltzmann-Gibbs, Renyi and Tsallis, definitions of entropy are introduced. Properties of these (and other) entropies are then reviewed and several physical applications of Tsallis entropy are described.  The author even discusses the role of entropy functionals in mathematics, chemistry, economics, biology, computer sciences, random networks image and signal processing and engineering.

The paper is very well written, thorough and yet easy to follow. The important points are illustrated by example calculations and graphs. Furthermore, it includes an extensive list of references.

Aside from being an excellent review, the paper makes a compelling case for the special status of the Tsallis entropy among the myriad of entropy functionals proposed in the literature. This is supported by a comparison of general properties of various proposals as well as by an analysis of many specific cases, both from physics and beyond.

For these reasons, I recommend the paper to be accepted in its present form.

Author Response

I am grateful to the Referee for his/her kind and stimulating words.

Reviewer 3 Report

The content of the paper is well organized. The theory part of the paper is substantial. The description of entropy is well supported by data. So, this paper can be accepted directly without revision.

Author Response

I am grateful to Referee 3 for his/her kind and stimulating words.

Round 2

Reviewer 1 Report

It can be accepted in this form.