Wave–Particle Duality and Horizon Thermodynamics from Entropy Geometry: Unifying Quantum Optics and Gravitational Structure in TEQ

We show that the phenomenon of wave–particle duality in quantum optics and the entropy structure of black hole horizons can be traced to the same underlying geometric mechanism in the Total Entropic Quantity (TEQ) framework: finite entropy curvature governing stable distinguishability. By analyzing the transverse entropy geometry of photons at the resolution boundary, we derive that their Fourier structure exhibits an exponential cutoff imposed by entropy curvature, a structure mirrored in the transverse mode profile of horizon thermodynamics. This correspondence is derived from the entropy-weighted path integral and the entropy curvature operator in the TEQ framework, and is shown to hold for all systems with collapsing longitudinal resolution. Thus, both photon wave structure and black hole horizon entropy are unified, within TEQ, as manifestations of the same entropy-geometric resolution limit. Several empirical phenomena, currently lacking complete explanations, are discussed as potential applications.