  Although the fundamental equations of ordinary thermodynamic systems are
known to correspond to first-degree homogeneous functions, in the case of
non-ordinary systems like black holes the corresponding fundamental equations
are not homogeneous. We present several arguments, indicating that black holes
should be described by means of quasi-homogeneous functions of degree different
from one. In particular, we show that imposing the first-degree condition leads
to contradictory results in thermodynamics and geometrothermodynamics of black
holes. As a consequence, we show that in generalized gravity theories the
coupling constants like the cosmological constant, the Born-Infeld parameter or
the Gauss-Bonnet constant must be considered as thermodynamic variables.
