Comment on “Essential discreteness in generalized thermostatistics with non-logarithmic entropy” by Abe Sumiyoshi

Abstract

This is an unusual comment. Acting as a referee for the paper in question [1], I had serious fundamental misgivings against which prof. Abe argued forcefully. The editor-inchief of EPL thought that this fundamental disagreement would be of interest to readers of this journal and invited an open comment-reply. I accepted to forego my referee anonymity and have collected my concerns below. Let me also emphasize that I have no axe to grind in the long debate pro et con q-entropies (Tsallis entropies); I do not belong to any of those schools. The sole stated reason for dismissing q-entropies for continuous systems in [1] is that such entropies would be “non-physical” which is later clarified to mean that they would contain Planck’s constant h. What is physical or not is a matter of taste, except of course if the theory results in a contradiction to physical experiment. No such contradiction has been presented. However, one cannot axiomatically define what is physical. Further, it is very difficult to see why the presence of Planck’s constant should be a rigid disqualification. We have many classical physical expressions which contain natural constants like the speed of light, the elementary charge, etc. Dismissing a continuous formulation of q-entropies solely for being “non-physical” is a self-created problem due to an overly restrictive definition of what is “physical”. In the end experiment will answer that question. The now classical information-theoretic expression for entropy,