  In this paper we analyze some interesting features of the thermodynamics of
the rotating BTZ black hole from the Carath\'{e}odory axiomatic postulate, for
which, we exploit the appropriate Pfaffian form. The allowed adiabatic
transformations are then obtained by solving the corresponding Cauchy problem,
and are studied accordingly. Furthermore, we discuss the implications of our
approach, regarding the the second and third laws of black hole thermodynamics.
In particular, the merging of two extremal black holes is studied in detail.
