Entropy-history separation with residual memory disclosed

On the Bell input, the models are immediately distinguishable at the channel level: the preserving process has $I(S:R_{\mathrm{all}})=2\log d$, whereas the retaining process has $I(S:R_{\mathrm{all}})=0$ and $I(S:F)=2\log d$. Mixtures and reference-entangled inputs contain information absent from a list of pure-input scalar entropies.

Equal entropy histories are also weaker than equal complete record laws, and equal selected records are weaker than equal residual instruments. These distinctions parallel the complete-process and record interfaces in Psy02-B and En03-A CheungPsy02B,CheungEn03A.