Quantum-Corrected Thermodynamics and Phase Structure of Electrically Charged Kalb–Ramond Black Holes via GUP-Modified Tunneling

We study the semiclassical thermodynamics of the Duan–Zhao–Yang charged Kalb–Ramond black hole, in which a non-zero vacuum expectation value of a rank-two antisymmetric tensor field breaks local Lorentz symmetry through a parameter [Formula: see text]. The Hawking temperature [Formula: see text] follows from Hamilton–Jacobi tunneling and reduces to the Schwarzschild, Reissner–Nordström and neutral Kalb–Ramond limits in the appropriate corners of parameter space. The main clarification we offer concerns the electric potential conjugate to Q in the first law: it is the redshifted quantity [Formula: see text], not the Lagrangian-level Coulomb potential [Formula: see text]. An integrability check and a Wald-formalism derivation both confirm that only [Formula: see text] makes the thermodynamic one-form exact, recovers the Bekenstein–Hawking area law, and closes the Smarr relation [Formula: see text] without adding a Lorentz-breaking pressure term. With the Ali–Das–Vagenas generalized uncertainty principle and [Formula: see text] we obtain closed forms for the GUP-corrected temperature, entropy, internal energy, Helmholtz and Gibbs free energies, and heat capacity. The Davies-type divergence sits at [Formula: see text], the Joule–Thomson inversion temperature reads [Formula: see text], and [Formula: see text] shifts the phase-transition structure analytically. The quantum-gravity terms enter at orders [Formula: see text] and [Formula: see text] with a logarithmic coefficient [Formula: see text] that is independent of [Formula: see text] and [Formula: see text]; the Schwarzschild limit reproduces the Anacleto–Brito–Passos result.