  The physics of many materials is modeled by quantum many-body systems with
local interactions. If the model of the system is sensitive to noise from the
environment, or small perturbations to the original interactions, it will not
properly model the robustness of the real physical system it aims to describe,
or be useful when engineering novel systems for quantum information processing.
We show that local observables and correlation functions of local Liouvillians
are stable to local perturbations if the dynamics is rapidly mixing and has a
unique fixed point. No other condition is required.
