From a grammatical point of view (Michael Halliday’s Systemic Functional Grammar lays this out), the original question is missing important pieces of information which can be misleading both to the speaker and reader.
“How is it that a wide variety of physical systems can Represent the same idea?”
Can physical systems represent?
They cannot. Who can? Humans can.
So, that is how I’m starting.
From that point, I can build further.
Humans represent a wide variety of physical systems by the same idea.
For what reasons do we do so?
Humans are pattern seekers. We are sense-makers. This is observably true through our creation of complex representative languages which take observed and experienced phenomenon and substitute grunts and scribbles to stand-in-place of moving or touching or interacting with such things directly.
Language is faster than physical movement.
In our sense-making, we notice similar lines of motion among otherwise distinctive systems.
We notice they perform similar functions within their own systems.
So, we can represent a wide variety of physical systems by the same idea.
We’ve formalized much of it in mathematics, which is an even more succinct way to manipulate symbols instead of objects.
So, what now? What do we do with these similarities (say, between, hydraulic, electric, thermal and mechanical)?