2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200213We study the thermodynamics associated to topological black hole solutions of AdS gravity coupled to nonlinear electrodynamics (Born-Infeld) in any dimension, using a background-independent regularization prescription for the Euclidean action given by boundary terms which explicitly depend on the extrinsic curvature (Kounterterms series). A finite action principle leads to the correct definition of thermodynamic variables as Noether charges, which satisfy a Smarr-like relation. In particular, for the odd-dimensional case, a consistent thermodynamic description is achieved if the internal energy of the system includes the vacuum energy for AdS spacetime.29 pages, no figures; additional comments on extreme black hole case, a few references added; final version for PRDHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext