2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/19407We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant $q$-exponential distribution reveal that the connection of the current nonextensive statistical mechanics to thermodynamics might be disturbed by this invariance.14 pages, no figure, RevTeX fileStatistical Mechanicstext