Quasi-homogeneous geometrothermodynamics of a noncommutative Reissner–Nordström black hole

We present the thermodynamic properties of a noncommutative Reissner–Nordström (NCRN) black hole (BH) modeled with Lorentzian distributions. The analysis is carried out using a Legendre-invariant formalism called Geometrothermodynamics (GTD) which is applied to a quasi-homogeneous system generated by the NCRN BH. This formalism enables the study of phase transitions by locating Ricci scalar singularities, from which the phase transition points are determined in terms of the thermodynamic variables. We also examine how the noncommutative (NC) parameter [Formula: see text] can be interpreted as a thermodynamic variable within quasi-homogeneous thermodynamic laws, highlighting its potential role on phase transitions beyond those well-known characterized by divergences in the heat capacity.