Validity of the third law of thermodynamics for the Tsallis entropy

Bento et al. [Phys. Rev. E 91, 022105 (2015)PLEEE81539-375510.1103/PhysRevE.91.022105] recently stated that the Tsallis entropy violates the third law of thermodynamics for 0<q<1 in the subadditive regime. We first show that the division between the regimes q<1 and q>1 is already inherent in the fundamental incomplete structure of the deformed logarithms and exponentials underlying the Tsallis entropy. Then, we provide the complete deformed functions and show that the Tsallis entropy conforms to the third law of thermodynamics for both superadditive q<1 and subadditive q>1 regimes. Finally, we remark that the Tsallis entropy does not require the use of an escort-averaging scheme once it is expressed in terms of the complete deformed functions.