Reply to “Comment on ‘Third law of thermodynamics as a key test of generalized entropies’ ”

Abstract

In Bento et al. [Phys. Rev. E 91, 039901 (2015)] we develop a method to verify if an arbitrary generalized statistics does or does not obey the third law of thermodynamics. As examples, we address two important formulations, Kaniadakis and Tsallis. In their Comment on the paper, Bagci and Oikonomou suggest that our examination of the Tsallis statistics is valid only for q≥1, using arguments like there is no distribution maximizing the Tsallis entropy for the interval q<0 (in which the third law is not verified) compatible with the problem energy expression. In this Reply, we first (and most importantly) show that the Comment misses the point. In our original work we have considered the now already standard construction of the Tsallis statistics. So, if indeed such statistics lacks a maximization principle (a fact irrelevant in our protocol), this is an inherent feature of the statistics itself and not a problem with our analysis. Second, some arguments used by Bagci and Oikonomou (for 0<q<1) reflect a misunderstanding of our explicit calculations. These arguments are then clarified under our approach and illustrated through a simple two-level system.

Validity of the third law of thermodynamics for the Tsallis entropy

“…[7], since it should be satisfied for any Hamiltonian independent of modelling short-range or long-range interactions. Therefore, it is worth careful study and analysis [8,9].…”