Entropy-Geometric Branch Selection in the Everettian Branch Measure: A C=1 Framework

Abstract

The Everettian interpretation of quantum mechanics provides a unitary account of branching quantum histories but leaves open questions concerning the relative significance of branches and the emergence of observer measures. We develop an entropy-geometric extension of the Everettian Branch Measure (EBM) framework based on the microscopic C=1 theory of coherence dynamics. A saddle-point expansion of the entropy-weighted partition functional yields branch amplitudes carrying an entropy-dependent factor: |A_i|²=|N_i|²exp(−2ΔS_i/k_B). The Born rule, Observer Measure Principle, and Past Hypothesis remain explicit postulates. v2 consolidated correction (Aug 2026), three items: (1) The entropy functional, originally an abstract two-level-system expansion applied without justification to the continuum coherence field, is repaired by identifying the field with a weak-coupling BCS order parameter — an explicit, stated modeling choice. (2) The soliton benchmark (ΔS=−5.39 k_B) is relabeled illustrative-only: under the repaired entropy functional, no legitimate stable benchmark soliton exists at any coupling ratio — the sech(u) profile previously used is a saddle-point (vacuum-decay "bounce") configuration, not a stable bound state. (3) Two technical gaps in the saddle-point derivation are addressed: an explicit scale-comparability assumption is added to justify the entropy/dynamics decoupling, and an apparent fluctuation-determinant double-counting is shown to be a non-issue (the entropy-curvature contribution is a pure phase at leading order). None of these changes affect the central branch-amplitude formula. What remains open: no legitimate physically-derived benchmark soliton currently exists for this framework — flagged as future work.