Phase Coherence Probabilities

Phase Coherence Probabilities are the normalized measures P_ij, between 0 and 1, of how well the phases of two binary Pulse units i and j are aligned; they are the probabilities from which the book computes computational entropy. The book redefines entropy as phase misalignment. Classical entropy counts accessible microstates, S● = k_B × ln(Ω); BPT computational entropy instead measures lost coordination between Pulse units, weighting the logarithm of each pair's coherence probability by their correlation coefficient. The result is entropy as deterministic desynchronization rather than random fluctuation, tied to Recursive State Evolution S(n+1) = F[S(n), H(n), ℜₙ] and aligned with Shannon's information entropy. Perfect alignment makes each logarithm zero and contributes no entropy; poor alignment raises it. The book writes S☫ = -Σ_{i,j} C_{ij} × ln(P_{ij}) / ln(2), where S☫ is BPT computational entropy [∅], C_ij the correlation coefficients between Pulse units i and j [∅], P_ij the normalized Phase Coherence Probabilities in [0,1] [∅], i and j the Pulse unit indices [∅], and ln the natural logarithm. Phase Coherence Probabilities connect to Phase Drift Propagation, Phase Coherence, Recursive State Evolution, Characteristic Drift Time Scale and Energy-Information Equivalence.