Entropy Leakage vs Invariant Modes: Finite Boundaries in Electron Diffraction

Conventional diffraction theory interprets fading amplitudes as probabilistic tails that extend indefinitely, treating background scatter as hidden randomness. We present an alternative framework that distinguishes invariant modes—the reproducible carriers of structure—from entropy leakage, the diffuse energy that does not contribute to coherence. Using 300 keV scanning transmission electron microscope holography (STEMH) of FeGd magnetic specimen, we perform phase reconstructions and identify iso-magnetic contours that persist across boundaries and internal features. These contours represent invariant modes, sharply bounded and finite. Residual scatter is not unresolved probability but entropy leakage, physically present yet structurally absent. This distinction predicts measurable diffraction cutoffs and provides a deterministic reinterpretation of noise in quantum interference. By isolating entropy from invariance, our results offer both a new calibration method for electron microscopes and a pathway toward non-probabilistic interpretations of quantum measurement.