Reply to "Comment on 'Third law of thermodynamics as a key test of generalized entropies' ".
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.
Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil.
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Bento
National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil.
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Viswanathan
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba-PR, Brazil.
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da Luz
Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil and Departamento de Física, Universidade do Estado do Rio Grande do Norte, 59610-210 Mossoró-RN, Brazil.
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Silva