Homothetic motions and Newtonian cosmology

We study the thermodynamics and the different thermodynamic geometric methods of Reissener-Nordström-de Sitter black hole and its extremal case, which is similar to the de Sitter black hole coupled to a scalar field, rather called an MTZ black hole. While studying the thermodynamics of the systems, we could find some abnormalities. In both cases, the thermodynamic geometric methods could give the correct explanation for all abnormal thermodynamic behaviors in the system.