bellPairEntropy
plain-language theorem explainer
The definition sets the entanglement entropy of a Bell pair to log 2. Researchers deriving Bell inequality violations from shared ledger entries cite this constant when bounding quantum correlations or applying monogamy relations. The assignment is a direct constant chosen to match the von Neumann entropy of the two-qubit singlet state.
Claim. The entanglement entropy of a Bell pair is $S = log 2$.
background
Entropy in Recognition Science measures total defect in a configuration, with zero defect yielding minimum entropy. Upstream definitions include entropy as total_defect for initial conditions, entropy as beta times average energy plus log of the partition function in Boltzmann systems, and the analogous form k_B (log Z + beta average energy) for discrete systems. The BellInequality module treats entanglement as shared ledger entries between particles created together, which produce non-local correlations while forbidding signaling and classical local realism.
proof idea
The definition is a direct assignment of the constant Real.log 2. It anchors the base case for the subsequent theorem establishing maximal entanglement entropy.
why it matters
This supplies the numerical value used in the theorem max_entanglement_entropy that proves maximally entangled states have entropy log(d) for d=2. It supports the module target of deriving Bell inequality violation from ledger structure and connects to the Tsirelson bound of 2 sqrt(2). It touches the open question of how ledger exclusivity enforces monogamy of entanglement.
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