I found a few new concepts for tracking.
There is computational mechanics, which deals with numerical modeling of mechanical processes and there is an article about it on the wiki. This post is not about it.
This post is about computational mechanics, which studies abstractions of complex processes: how emergent behavior arises from the sum of the behavior / statistics of low-level processes. For example, why the Big Red Spot on Jupiter is stable, or why the result of a processor calculations does not depend on the properties of each electron in it.
The concept of a device that can exist in a finite set of states and can predict its future state (or state distribution?) based on the current one.
Computational mechanics allows (or should allow) to represent complex systems as a hierarchy of ε-machines. This creates a formal language for describing complex systems and emergent behavior.
For example, our brain can be represented as an ε-machine. Formally, the state of the brain never repeats (voltages on neurons, positions of neurotransmitter molecules, etc), but there are a huge number of situations when we do the same thing in the same conditions.
Here is a popular science explanation: https://www.quantamagazine.org/the-new-math-of-how-large-scale-order-emerges-20240610/
P.S. I will try to dig into scientific articles. I will tell you if I find something interesting and practical. P.P.S. I have long been thinking in the direction of a similar thing. Unfortunately, the twists of life do not allow me to seriously dig into science and mathematics. I am always happy when I encounter the results of other people's digging.