  Due to the asymptotic structure of the black hole solution, there are two
different thermodynamic schemes for the charged Banados-Teitelboim-Zanelli
(BTZ) black hole. In one scheme, the charged BTZ black hole is super-entropic,
while in the other, it is not (the reverse isoperimetric inequality is
saturated). In this paper, we investigate the thermodynamic curvature of the
charged BTZ black hole in different coordinate spaces. We find that in both
schemes, the thermodynamic curvature is always positive, which may be related
to the information of repulsive interaction between black hole molecules for
the charged BTZ black hole if we accept an empirical relationship between the
thermodynamic curvature and interaction of a system. More importantly, we
provide a diagnosis for the discrimination of the two schemes from the point of
view of the thermodynamics geometry. For the charged BTZ black hole, when the
reverse isoperimetric inequality is saturated, the thermodynamic curvature of
an extreme black hole tends to be infinity, while when the reverse
isoperimetric inequality is violated, the thermodynamic curvature of the
extreme black hole goes to a finite value.

General Relativity and Quantum Cosmology;High Energy Physics - Theory