Absorbing Sub-loops and Resonance Decay

This work presents a rigorous analysis of a class of finite-dimensional open quantum systems governed by Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations with constrained coupling structure. The system Hilbert space is decomposed into a preferred subspace and its orthogonal complement, and a population functional (“resonance”) is introduced to measure support on the preferred subspace. Under explicitly stated axioms—block-diagonal Hamiltonian dynamics, one-way dissipative coupling without reciprocal pumping, and bounded control incapable of restoring population once fully lost—we prove that the resonance functional is monotonically non-increasing and that the zero-resonance set constitutes a forward-invariant absorbing subset of state space. This establishes the existence of absorbing sub-loops and unavoidable state-space bifurcation into disjoint invariant basins. A maximally mixed, backbone-supported fixed point is introduced as a natural equilibrium state within the preferred subspace. Canonical qubit and multi-level examples are provided to illustrate the general results. The framework is fully falsifiable: violation of any coupling constraint eliminates monotonicity and trap invariance. The paper is purely mathematical and physical in scope. It makes no metaphysical or interpretive claims and is intended as a contribution to the theory of open quantum systems, invariant subspaces, and irreversible dynamics.