Why it is a question
THEORY-030 now holds a derivation: if a memory and everything it can dump entropy into evolve reversibly, starting uncorrelated, then a step that loses H(X | f(X)) of logical distinguishability must raise the environment’s entropy by at least that much, k ln 2 per bit, and a step that is injective on the logical states has no floor. That is a theorem about the stated dynamics. Bennett presents the principle as a restatement of the Second Law, concedes the Earman–Norton dilemma “with some justice”, and Norton calls the literature “too fragile” (LIT-114 §7.2). The derivation assumes the very reversibility that dilemma questions. Until 2026-10-20 this was THEORY-030’s promote_when.
What would answer it
- A derivation of the same bound from weaker assumptions, or a reading of Earman and Norton that shows the reversible-dynamics derivation circular.
- A demonstrated positive lower bound on the entropy cost of a logically reversible operation, or an erasure of unknown data done with less than k ln 2 of entropy export per bit; either would refute the account.
- A close reading of Landauer 1961 (LIT-328), which would add the original statement but not settle the question.