Geometric Dynamics and Thermodynamics in Constrained Null Geometry: First Loss, Rank Change, Invariant-Preserving Reconstruction, and D–T Fusion

Abstract

This work develops a unified geometric framework for dynamics and thermodynamics in Constrained Null Geometry (CNG) and applies it to deuterium–tritium fusion as a complete worked example. The thermodynamic sector is derived from the admissible CNG domain and its induced measure. Entropy is identified with the logarithmic realization volume of a current-geometry equivalence class, temperature follows from the energy dependence of that volume, and the canonical ensemble follows from reservoir counting. Changes of internal energy are separated into redistribution within a fixed geometry and geometric work produced by deformation of the admissible domain or operator. Complete norm-preserving transport is entropy neutral, while current-geometry reduction produces a non-negative relative-entropy contribution and yields a CNG transport–quotient H-theorem. Near equilibrium, relaxation separates into entropy-neutral geometric transport and positive relaxation. For an open sector, the exact physical decay or relaxation rate is given by outward event flux divided by surviving sector weight. This relation does not require exponential decay or a resonance-pole assumption. The D–T sector provides an explicit rank-changing event. The separated deuterium–tritium geometry is carried by the non-additive [3,2] sector and reaches first loss when that separation sector vanishes. Conventional preparation and titanium admissibility control are shown to be distinct access mechanisms to the same intrinsic event. For the canonical hcp alpha-titanium monovacancy carrier, the complete fourteen-cell geometry gives a one-sided hard-switch result with cell admissibility equal to 1 and a conservative geometric margin of 1/3, together with an explicit exterior falsifier. After the finite 5-to-4-plus-1 reconstruction, the external alpha–neutron state is derived on its own relativistic rest-screen geometry rather than by carrying the internal D–T geometry forward. The resulting exact two-body pushforward gives the central result: the internal and external geometries are different, while the complete event invariant is preserved and the total inner-to-outer energy Jacobian is exactly one. The result shows that a CNG event may change its realized geometric carrier without changing its complete physical invariant. D–T fusion therefore provides a concrete connection between first loss, finite event time, rank-changing reconstruction, external product geometry, relaxation, and thermodynamic redistribution without using force, Coulomb-barrier, fitted nuclear-radius, or phenomenological potential assumptions as intrinsic premises.