Holomorphic Entropy
Holomorphic Entropy (IV.D80) is the holomorphic sector of the τ-Entropy Splitting (IV.D24): the count of breathing modes of a defect bundle that are compatible with holomorphic boundary data. It is the τ-categorical analog of the chiral half of conformal entropy and the natural quantity for τ-quantum-information.
τ-Definition
Holomorphic Entropy (IV.D80) is the holomorphic sector of the τ-Entropy Splitting (IV.D24): the count of breathing modes of a defect bundle that are compatible with holomorphic boundary data. It is the τ-categorical analog of the chiral half of conformal entropy and the natural quantity for τ-quantum-information.
Categorical invariant. S_hol(B) := log #{breathing modes of B compatible with holomorphic boundary data}; the holomorphic half of the Entropy Splitting decomposition.
Primary registry anchor:
IV.D80
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D466— Total Entropy as breathing-mode count -
IV.D24— Entropy Splitting: S = S_hol + S_antihol -
IV.D80— Holomorphic Entropy — the holomorphic-sector half -
IV.P30— Entropy-Mode-Count Bound caps S_hol by holomorphic dimensional capacity
Lean modules referenced:
TauLib.BookIV.QuantumMechanics.EnergyEntropy
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- k_B via τ-conjugate ratio between energy and breathing-mode count
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-energy-entropy.tex
Lean Coverage
See Also
Related glossary entries
Cross-domain bridges
This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.