Thermodynamic Criticality and Phase Transitions in Dilaton Black Holes with Nonlinear Electrodynamics: A Geometrothermodynamics Study

We investigate the thermodynamic criticality and phase structure of dilaton black holes in the presence of Born-Infeld nonlinear electrodynamics and a Liouville-type potential. By adopting an analytical approach based on the near-horizon geometry and the first law of thermodynamics, we derive consistent expressions for temperature, entropy, charge, and mass. This method allows us to bypass the complexity of finding a global closed-form metric solution while maintaining exact thermodynamic consis