Reply to the comment on 'Route from discreteness to the continuum for the Tsallis $q$-entropy' by Congjie Ou and Sumiyoshi Abe
| Autor: | Oikonomou, Thomas, Bagci, G. Baris |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 97, 066102 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.97.066102 |
| Popis: | It has been known for some time that the usual $q$-entropy $S_q^{(n)}$ cannot be shown to converge to the continuous case. In [Phys. Rev. E 97 (2018) 012104], we have shown that the discrete $q$-entropy $\widetilde{S}_q^{(n)}$ converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [Phys. Rev. E 97, (2018) 066101, arXiv:1801.03035] noted that this form of the discrete $q$-entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability property by the discrete $q$-entropy strongly depends on the origin of the convergence factor, presenting an example in which $\widetilde{S}_q^{(n)}$ is expandable. Comment: 2 pages, Accepted in Physical Review E |
| Databáze: | arXiv |
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