Quantum Tunneling and Bound States from Entropy Geometry: A TEQ-Based Derivation

We derive quantum tunneling probabilities and bound-state quantization directly from the entropy-weighted path integral and entropy curvature principles of the Total Entropic Quantity (TEQ) framework. Instead of invoking traditional quantum postulates such as wavefunctions, operator algebra, or boundary-condition quantization, we demonstrate that exponential suppression of entropy-unstable trajectories in high-curvature entropy geometries naturally produces canonical tunneling profiles and energy discretization. Standard quantum results—including the WKB tunneling formula and the Bohr–Sommerfeld quantization rule—are recovered explicitly as special limiting cases of a broader variational principle grounded in entropy geometry. These results provide structurally grounded, empirically falsifiable predictions distinct from conventional quantum mechanics, testable in engineered nanoscale and quantum optical systems.