  In this work, we investigate the thermal properties of black holes using a
new class of generalized entropy functions [K. Ourabah, Class. Quantum Grav.,
41, 015010 (2024)]. At the fundamental level, these entropic forms are
associated with alternative gravitational laws, within an entropic gravity
framework. Our investigation revolves around three distinct entropy functions
associated with the Yukawa Potential Correction, Non-local Gravity Correction,
and Gradient Field Gravity Correction. Through comparative analysis, we study
how such entropic constructs impact the thermodynamic behavior of black holes.
For each case, we derive the stability thermodynamic conditions associated with
the respective entropic constructs.
