"Negative Derivatives" -> Integrals? Is this a thing? I would just say the integrals of position, in the same way jerk is the derivative of acceleration. I have heard "anti-derivative" as well.

Pipe organs and other flow based instruments were the examples I remember from when I last looked up uses for absement. The volume is based on the position of a key, which allows flow to build up in a pipe, which is proportional to how far down the key is pressed (ie, the integral of key position).

This was posted in a similar question and has a lot of good info, except for the 2nd integral of position except to say that there is a two staged absement instrument (so, what would be the sound output actually controls the "key" for the next stage of the pipe...). It's pretty contrived.