Temperature
Temperature in the τ-framework is the defect-gradient quantity (IV.D228): the τ-internal gradient of the breathing-mode population on a defect bundle. It is not fundamental — it is a derived conjugate variable to entropy, with no negative values admitted (IV.R168).
τ-Definition
Temperature in the τ-framework is the defect-gradient quantity (IV.D228): the τ-internal gradient of the breathing-mode population on a defect bundle. It is not fundamental — it is a derived conjugate variable to entropy, with no negative values admitted (IV.R168).
Categorical invariant. Temperature(B) := ∂E/∂S evaluated on bundle B = the conjugate of entropy under the τ-thermodynamic Legendre structure; equivalently, the τ-defect-gradient.
Primary registry anchor:
IV.D228
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D466— Entropy as breathing-mode multiplicity -
IV.D228— Temperature as τ-defect-gradient — the conjugate of entropy -
IV.R154— Temperature is not fundamental — it is derived from S and E -
IV.R168— No negative temperatures — the gradient is sign-definite
Lean modules referenced:
TauLib.BookIV.QuantumMechanics.EnergyEntropy
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- k_B := τ-conjugate ratio between energy and breathing-mode count
- T := (∂E/∂S) evaluated on the τ-state
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-energy-entropy.tex