In the Topological Knot Quantum Theory (TQNT), electrical conduction is the incoherent regime of the chi-well dance: the electron is scattered at each recapture, at the decoherence rate Gamma = 1/tau. This note shows that the entire thermodynamics of a conductor follows from this single quantity. Master formula (heat). Under a field, the electron acquires an ordered drift velocity between decoherence events; in steady state this drift energy is transferred to the lattice at each event. The power dissipated per unit volume is qdot = (m*/n e²) Gamma J² = rho J²: the heat released is proportional to the decoherence rate Gamma. Decoherence converts ordered drift (drawn from the field) into disordered vibration of the lattice wells (phonons). Master formula (entropy) and the second law. Dividing by temperature gives the entropy production rate Sdot = qdot/T = (m*/n e² T) Gamma J² >= 0. Since all factors are positive, the sign of Sdot is that of Gamma, so the second law coincides exactly with the irreversibility of decoherence: Sdot >= 0 if and only if Gamma >= 0. The dance can only lose its coherence, never spontaneously regain it; the arrow of time is this loss of coherence. Reversible limit. Superconductivity (Gamma = 0, coherent dance with topological phase lock) is the reversible limit: neither heat nor entropy production. First law and runaway. The energy balance rhoₘ cₚ dT/dt = qdot - qdotₗoss (T), with Gamma (T) ~ T at high temperature (linear resistivity), produces the positive feedback driving thermal runaway and fusion at high power. What heat is. Heat is the disordered vibration of the lattice chi wells (phonons), not a violation of the wells; the wells are set into vibration but remain intact. The only true violation is melting, when the vibration amplitude reaches a fraction (~10 %, Lindemann) of the inter-well spacing. Honest status. The transport expressions coincide with the Drude-Joule form; the specific contribution is the identification of Gamma as the dance's decoherence rate and of Gamma = 0 as the topologically protected coherent (superconducting) limit, from which Sdot >= 0 Gamma >= 0 follows. The Gamma (T) dependence belongs to the full microscopic calculation. Contents. FR + EN LaTeX sources and PDFs of the dissipation master-formula note, plus the reproducible script (thermodynamicsdecoherencechi. py). Companion deposits (separate): the electronic-bipolaron synthesis and the superconductivity letter.
Lilian Cariou (Fri,) studied this question.