Extrinsic gene-expression noise (${\eta }_{\mathrm{ext}}^2=⟨xy⟩-1$)

Expression fluctuations caused by shared variation in cellular conditions, such as expression machinery or growth state. Matched reporters tend to co-vary. For mean-normalized reporters whose intrinsic components are conditionally independent, the squared extrinsic noise equals $⟨xy⟩-1$.