Interesting difference between an engineering perspective and a physicist's perspective. Engineering relies on the idea of state variables which are independent and have a time evolution described by a first order differential equation.
Physicists prefer constructing a description of a state using known conservation laws and allow for couplings to be described as needed. They do not require the time evolution of the variables have first order differential equations.
The difference is bcoz engineers like to control the system, and physicists want to try to understand it. If the conservation laws do yield couplings and variables that are readily "smushed" into a state variable, then the engineering of the system is frustrated.
In this situation a Physicist will try to drive the system description to a place where all the couplings are captured correctly. The Physicist will do so hoping that eventually even though the underlying time evolution is not first order, it can be approximated as first order
over a small enough interval of time (influenced heavily by the couplings) & the resulting set of equations can somehow be diagonalized to produce a set of eigenvectors that can be used as state variables. This may turn out to be a good hope if not all couplings are discoverable.
To the engineering mindset - what the Physicist is doing will seem insane and nonsensical. A reasonable counter argument that will emerge will be that knowledge of all the couplings is impossible so a search of this nature is doomed to fail.
Another argument one will hear is that the linearlization of the time evolution is possible only over time intervals which are too narrow to be practical and that such a system cannot be engineered as the evolution (upon interaction with the feedback) will be chaotic.
Wow... this thread is quickly turning into my gripes with life as physicist in industry but yeah I think this may apply in other places as well.
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