To clarify the question, by "systems of laws" I mean something like the collection of physical laws that govern nature, rules of a game like soccer or chess, or a power system that governs what fictional characters can do in a novel/video game.
Basically, it's a set of statements about an entity that are always true, and from which every possible event that could happen in the entity can be deduced; if it helps, think of them as a logic analogue of a Cartesian coordinate system. I think the concept of axioms comes close to what I'm going for, but I don't know what the branch of math they belong to is called, or if there are any other branches or theories that detail what I need better.
A few candidates:
Abstract algebra: If the "operations" satisfy certain laws (e.g. commutative, associative, has identity/inverses, etc), then what? E.g. The Rubik's Cube is governed by its symmetric group.
Dynamical System: If we know the current status of the system, and its trend (derivative or infinitesimal change), then what? E.g. chaos theory, Poincaré recurrence theorem, ergodicity, etc.
Game Theory: E.g. Zermelo's theorem can be applied to chess or any finite combinatorial game.
Computer Science: What a Turing machine (which is set up by just a few rules) can/cannot do (in polynomial time)? What about qubits?
In fact, I would argue the axiomatic method is about to understand the behavior of systems under certain laws: I don't care what kind of "materials" your system is made of (it can be atoms as in physics, or texts/proofs as in mathematical logic), but as long as it satisfies this and that rule, I can tell you it must also ...
This question also reminds me of the constructo theory, but I really have no idea what it it.