One of the examples given on Twitter that I found enlightening (not an expert so I hope I'm interpreting this correctly): if you have a homeostatic system, you would specifically expect to find less correlation between the components than between causally unrelated quantities (e.g. when the correlation between the position of a chicken's body the position of the same chicken's head is lower than the correlation between the position of the chicken's body and a different chicken's head: https://imgur.com/gallery/vgcxL)