Comment on “Critique of q-entropy for thermal statistics”

It was recently argued [M. Nauenberg, Phys. Rev. E 67, 036114 (2003)] that the theory sometimes referred to as nonextensive statistical mechanics has no physical basis, for a considerable variety of reasons, including the impossibility of measuring the temperature out of the Boltzmann-Gibbs (BG) theory. We comment here on virtually all the physically and mathematically relevant issues, and point out what we consider to be severe inadvertences contained in that paper. In particular, we factually argue, through computer simulations, the validity of the zeroth principle of thermodynamics, and of the basic rules of thermometry for nonextensive systems. This fact further supports the possible connection with the thermodynamics of nonextensive statistical mechanics, which is already known to be consistent with the first, second, and third principles. All the foundational steps (e.g., the uniqueness of the entropy and the stationary state distribution) have already been established for nonextensive thermostatistics on similar grounds than those long known for BG statistics, the former corresponding to power laws (expected for long-range interactions when size N diverges before time t), and the latter correspond to the BG exponential law (expected for long-range interactions when N diverges after t, as well as for short-range interactions in any diverging order for N and t). We conclude that the invalidating arguments made by Nauenberg by no means apply.