Reply to the comment on “Route from discreteness to the continuum for the Tsallis q-entropy” by Congjie Ou and Sumiyoshi Abe

Abstract

It has been known for some time that the usual q-entropy Sₙ(q) cannot be shown to converge to the continuous case. In Phys. Rev. E 97 (2018) 012104, we have shown that the discrete q-entropy Seₙ(q) converges to the continuous case when the total number of states is properly taken into account in terms of a convergence factor.

Ou and Abe [Phys. Rev. E 97 (2018) 066101] 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 non-fulfillment of the expandability property by the discrete q-entropy strongly depends on the origin of the convergence factor, presenting an example in which Seₙ(q) is expandable.