Shannon Entropy
H(X) — uncertainty in an outcome; information gained on observation
Shannon entropy H(X), from Claude Shannon’s 1948 theory, measures how uncertain a random outcome is — equivalently, how much information is gained when it is observed.
A deterministic step has zero stochastic entropy relative to its inputs (η = 1). That is not the same as sitting at L0: logical inference generalizes above concrete atoms and is typically L1 or L2. A fair coin has maximum entropy for a binary variable. A fraud model score sits between — uncertain, but not uniformly so. Entropy links formal information theory to the epistemic uncertainty facet: probabilistic L2 outputs carry positive entropy even with complete inputs.
Corpus stance
A1 — adopted on this site: Formal measure behind informal U bands and η loss; see What Information Theory Says.