Wald Entropy in Extended Modified Myrzakulov Gravity Theories: \(f(R, T, Q, R_{\mu \nu }T^{\mu \nu }, R_{\mu \nu }Q^{\mu \nu }, \dots )\)

We investigate black hole entropy in a broad class of modified gravity theories defined by generalized Lagrangians of the form \(\mathcal {L} = \alpha R + F(T, Q, R_{\mu \nu }T^{\mu \nu }, R_{\mu \nu }Q^{\mu \nu }, \dots )\), where \(R\), \(T\), and \(Q\) represent curvature, torsion, and non-metricity scalars. Using the vielbein formalism, we derive the Wald entropy for various subclasses of these models, extending the classical entropy formula to accommodate non-Riemannian geometry. Our focus is on how the additional geometric degrees of freedom modify the entropy expression. The analysis shows that such corrections arise systematically from the extended structure of the action and preserve diffeomorphism invariance. These results refine the theoretical framework for gravitational thermodynamics in extended geometry settings.