Derivation and Analysis of Deore's Equilibrium Constant and Deore's Unification Equation

This paper introduces a quantum-corrected form of the equilibrium constant,which we propose to name Deore’s Equilibrium Constant (KDeoreeq ), refiningclassical thermodynamic principles. Additionally, we extend our analysis to blackhole thermodynamics and singularity resolution. By modifying Einstein’s fieldequations, we derive what we call Deore’s Unification Equation, which successfully resolves singularities in black holes by introducing quantum curvaturecorrections. Our findings suggest experimental observability through gravitationalwaves and cosmic background radiation.