Pretty much anything can be considered as a "system," any aspect of it its "internal state," any aspect of it which can affect something else its "output," and any phenomenon that can affect it as "input" or "stimulus"On what grounds?
The fundamental problem here is that any definition broad enough to encompass everything that can be considered "computation" is going to be too broad to say anything meaningful about the nature of the class of phenomena it describes.
This is a matter of understanding how the phenomena work, not a matter of definition. Can you imagine someone 500 years ago saying "any definition of matter broad enough to encompass everything that can be considered 'matter' is going to be too broad to say anything meaningful about the nature of the class of phenomena it describes"?
But it wasn't a matter of "defining" matter, it was understanding how it worked, and the sort of understanding of matter we have these days -- at the level of protons, neutrons, and electrons, or deeper ones that that -- is very broad, yet very precise.
If you want to learn anything substantial, you'll generally have to pick some particular model of computation to study. You could choose to study deterministic pushdown automata, and then you will learn about computation that fits in that model. Or you could study Markov algorithms and learn about computation that fits in that model. Or you could even study something like Turing machines augmented with halting oracles. For computers that fit a particular model, you can discover things like what they can and can't compute, how quickly they can compute various things, what it takes to convert a computation system defined in that model into another model, etc., and this will all follow from properties of the model you've chosen to study.
It's entirely valid to investigate a particular model of computation as a means of better understanding computation. However, there's a really big danger in such an approach. If there is an underlying unity to the various types of computation, then investigating the specifics of a specific form of computation is likely to make you miss the forest for the trees. That is, if you're goal is to understand computation in general then you need to look at what is there in general, not what is a matter of just one specific way to do it. I do think that in order to understand computation its useful to look at the various forms of it, but to do so with an eye to what is fundamental and general across all the cases.
The only thing common to all models is that they have some way of mapping "input" to "output" via some change in "state." That is not specific enough to draw much further
insight...
Why do you think that? You don't say. I think that's an important hint about what computation -- all computation -- is doing.
(and FWIW, this is not a question about 'models' but about computation.. which is always a physical process. 'models' are a kind of computational device that can be used to perform that process).