Entropy
Entropy is the τ-categorical mode-counting invariant (IV.D466): for any thermodynamic τ-state it counts the breathing-mode multiplicity of the underlying defect configuration. It is bounded above by the Entropy-Mode-Count Bound (IV.P30) and split by the Entropy-Splitting Decomposition (IV.D24) into holomorphic and anti-holomorphic sectors.
τ-Definition
Entropy is the τ-categorical mode-counting invariant (IV.D466): for any thermodynamic τ-state it counts the breathing-mode multiplicity of the underlying defect configuration. It is bounded above by the Entropy-Mode-Count Bound (IV.P30) and split by the Entropy-Splitting Decomposition (IV.D24) into holomorphic and anti-holomorphic sectors.
Categorical invariant. Entropy(B) := log #{breathing modes of defect-bundle B compatible with thermodynamic state}; an E2 invariant satisfying the mode-count bound.
Primary registry anchor:
IV.D466
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D11— Physical Quantity Template defines dimensional invariants -
IV.D466— Entropy as breathing-mode multiplicity functional -
IV.D24— Entropy Splitting decomposes S into holomorphic + anti-holomorphic sectors -
IV.P30— Entropy-Mode-Count Bound caps S by the dimensional capacity of the defect -
IV.D80— Holomorphic Entropy is the holomorphic sector of the splitting
Lean modules referenced:
TauLib.BookIV.QuantumMechanics.EnergyEntropy
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- c, ℏ via IV.D293-D294
- k_B := categorical conversion factor between energy and τ-temperature defect-gradient
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-energy-entropy.tex