Perturbations of the specified dynamics

A bound only on a mixed environmental marginal is enough for the corresponding radiation-channel comparison. It is not, by itself, a comparison of chosen full complementary channels: their purifications and environmental identifications must also be specified.

The exact energy conservation of Theorem thm:evolution persists under a perturbation only if that perturbation also commutes with $H_0$. A small channel error is not an exact conservation law.