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We assume the validity of the Bekenstein-Hawking entropy, as given in terms of the horizon area of the Bardeen regular black hole, and consider it as the fundamental thermodynamic equation. We derive and investigate the behavior of the main thermodynamic variables. Using the formalism of geometrothermodynamics, we derive the geometric properties of the corresponding equilibrium space and show that the curvature contains information about the stability properties and phase transition structure of the black hole., Comment: New results and comments added. Typos corrected

We use the Legendre invariant formalism of geometrothermodynamics to investigate the geometric properties of the equilibrium space of a spherically symmetric phantom black hole with electric charge and dilaton. We find that at certain points of the equilibrium space, the thermodynamic curvature is characterized by the presence of singularities that are interpreted as phase transitions. We also investigate the phase transition structure by using the standard approach of black hole thermodynamics based upon the analysis of the heat capacity and response functions. We show compatibility between the two approaches. In addition, a new type of phase transition is found which is due to the presence of phantom energy and corresponds to a transition between black hole states with different stability properties., Comment: New appendices and comments added

We show that to investigate the thermodynamic properties of charged phantom spherically symmetric anti-de-Sitter black holes, it is necessary to consider the cosmological constant as a thermodynamic variable so that the corresponding fundamental equation is a homogeneous function defined on an extended equilibrium space. We explore all the thermodynamic properties of this class of black holes by using the classical physical approach, based upon the analysis of the fundamental equation, and the alternative mathematical approach as proposed in geometrothermodynamics. We show that both approaches are compatible and lead to equivalent results., Comment: 12 latex pages, no figures