Reply to "Comment on 'Route from discreteness to the continuum for the Tsallis q-entropy'

Abstract

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. E97, 012104 (2018), we have shown that the discrete q-entropy (S) over tilde ((n))(q) 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 [previous Comment, Phys. Rev. E 97, 066101 (2018)] 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 (S) over tilde ((n))(q) is expandable.