Generalized Entropies and Black Hole Area Quantization from Landauer's Principle

We investigate black hole area quantization by imposing Landauer's principle on the discrete entropy change between consecutive area levels. The elementary transition is identified with the entropy cost of erasing one bit of information, $\Delta S=k_B\ln 2$. For the Bekenstein--Hawking entropy, this gives the standard Bekenstein--Mukhanov value of the area spectrum parameter, which is used as the reference limit. The same discrete construction is then applied to generalized entropy functionals. For Barrow entropy, the parameter $\gamma$ becomes level dependent, while the relative separation between adjacent area levels still vanishes for large $n$. For the modified R\'enyi entropy, the nonsingular branch has vanishing relative spacing at large $n$, whereas the singular branch develops a finite-level pole. For the modified Kaniadakis entropy, the small $\kappa$ expansion shows that a fixed deformation parameter prevents the relative area spacing from vanishing in the large $n$ limit. Overall, the results suggest that Landauer's principle provides a useful framework for analyzing generalized entropic extensions of the Bekenstein--Mukhanov area spectrum.