Black Hole Thermodynamics in Energy-Efficiency Theory: The Slow Leak of Constrained-State Energy Through the Vacuum Gradient

Black hole thermodynamics—the Bekenstein-Hawking entropy formula and Hawking radiation—is one of the deepest bridges between general relativity, quantum mechanics, and thermodynamics. Yet the physical ontology behind these equations remains debated: what is the microscopic origin of black hole entropy? How does Hawking radiation preserve information? This paper develops an interpretation within Energy-Efficiency Theory (EET). Starting from Yang's Axioms, we define a black hole as an extreme concentration of constrained-state energy whose gravitational constraint barrier is the event horizon. The Bekenstein-Hawking entropy SBH=kBA/(4lPl2)SBH=kBA/(4lPl2) is derived as the constrained-state entropy ScSc of the horizon, where the area AA counts the number of microstates of the gravitational constraint. Hawking radiation is interpreted as the slow leakage of constrained-state energy through the free-state gradient of the vacuum, with the escape rate determined by the temperature TH=ℏc3/(8πGMkB)TH=ℏc3/(8πGMkB). The information paradox is resolved because the energy texture (information) of the infalling matter is not destroyed; it is encoded in the correlations of the emitted radiation. The total entropy S=Sc+Sf−ScorrS=Sc+Sf−Scorr increases, but information is conserved. The framework is fully compatible with general relativity at large scales and quantum mechanics at microscopic scales, providing a unified energy-ontological account of black hole thermodynamics.