Spectral Gap Formation, Resolvent Control, and the Stability of Classical Information in Open Quantum Systems

This work develops an operator-theoretic framework for the formation and stability of spectral gaps in open quantum systems and their role in preserving classical information. We show that resolvent control and pseudospectral bounds provide a precise mechanism for dynamical stability of low-energy subspaces under bounded non-selfadjoint perturbations. A classical record is defined operationally as a state whose distinguishability remains stable under such perturbations. Within this framework, we establish conditions under which spectral gap formation guarantees exponential suppression of leakage from the protected subspace, yielding robust persistence of macroscopic states. The analysis further connects spectral gap structure to dynamical stability and decoherence resistance in open quantum systems. These results provide a model-independent, operator-theoretic explanation for the emergence and persistence of classical information in physical systems, grounded in spectral properties rather than symmetry assumptions.