You want ecological theories, where the state space itself changes with each state.
There’s a number of those and I don’t know if they’re called ecological theories.
But that’s what biological modeling uses, as, for example, to model life on earth properly you have to take into account systems whose state space changes continually. Creatures born and die. Pollutants enter rivers and start affecting crops (life), which affect animals and insects eating crops, etc.
https://en.wikipedia.org/wiki/Systems_theory is a broad view. If you are working on an information theory whose state space itself changes with change, you can likely find your way through this route.
. In the case of an m-d system, each dimension has a state vector that contains the effect of prior inputs relative to that dimension. The collection of all such dimensional state vectors at a point constitutes the total state vector at the point.