  In this Letter we have shown that, from the standard thermodynamic functions,
the mathematical form of an equipartition theorem may be related to the
algebraic expression of a particular entropy initially chosen to describe the
black hole thermodynamics. Namely, we have different equipartition expressions
for distinct statistics. To this end, four different mathematical expressions
for the entropy have been selected to demonstrate our objective. Furthermore, a
possible phase transition is observed in the heat capacity behavior of the
Tsallis and Cirto entropy model.
