  In this paper, we show that 1) additive energy is not appropriate for
discussing the validity of Tsallis or R\'enyi statistics for nonextensive
systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or
entropy should be described by generalized statistics whose nature is
prescribed by the existence of thermodynamic stationarity. 3) the equivalence
of Tsallis and R\'enyi entropies is in general not true.
