Dissipation and identifiability of non-normal modes in Ornstein–Uhlenbeck processes

Nonnormality in a stable Ornstein–Uhlenbeck process governs both how a mode dissipates and whether it can be identified. We show that the second question, the conditioning of a mode, a diagonal entry of the Chalker–Mehlig overlap matrix read in the stationary-measure frame, is frame-variant and is not determined by the oscillatory–nonnormal decomposition of the entropy-production rate: at fixed dissipation the slow mode’s conditioning ranges over a bounded interval that the dissipation does not fix. The freedom is structural rather than generic. It is absent for two modes, where dissipation fixes conditioning, and appears only with a third mode and a nondegenerate spectrum, which supplies the compensating freedom. Two generators sharing the spectrum {0.5,1,2}but differing in conditioning exhibit it explicitl