3 Comment on “ Nonextensive hamiltonian systems follow Boltzmann ’ s principle not Tsallis statistics - phase transition , second law of thermodynamics ” by Gross

Recently, Gross claims that Boltzmann entropy S = k lnW is valid for any system at equilibrium, so that Tsallis entropy is useless in this case. I comment on some arguments forwarded to reach this conclusion and argue that the additive energy formalism of nonextensive statistics is not appropriate for the fundamental study of the theory for nonadditive systems. PACS : 02.50.-r, 05.20.-y, 05.30.-d,05.70.-a In his recent papers[1, 2, 3], Gross wrote “Boltzmann entropy is well defined, ...independently whether it is extensive or not... the eventual nonextensivity of Hamiltonian systems does not demand any exotic entropy at equilibrium”, “there is no alternative to the microcanonical Boltzmann statistics and to our geometrical foundation of equilibrium statistics”, “Therefore, for closed Hamiltonian many-body systems at statistical equilibrium, extensive or not, the thermo-statistical behavior is entirely controlled by Boltzmann’s principle...” and “nonextensive Hamiltonian systems do not demand a new entropy formalism like that by Tsallis”.