Just to wrap up this idea: "In spite of the etymology of the term, in
dynamics, a state is not stasis. Instead, it's ("simplified" or
"idealized") motion."
In principle, there's nothing that keeps you from defining this
simplified/idealized motion called "steady state" as complex/realistic
as you wish, provided you can make some sense of your model.
Steady states represent a system in motion, but in a type of motion
where some behavioral properties of the system are "stationary."
Hence the "steady" modifier. It's up to you, the theorist, to decide
which behavioral properties of a system to assume "stationary" and
which not.
A popular extension of the concept of steady state today is that of a
stochastic fixed point. In this case, a steady state is the motion
not of a single point but of, so to speak, the entire probability
distribution of a random variable. To get straight results (with the
math we have now), theorists usually restrict the stochastic
properties of the system to the well-known regular ones, the source of
randomness is assumed exogenous, etc. The world is always much
messier than this.
One may mock this and say that the drunkard is looking for his keys
where there's some light, not where he most likely lost them. But, in
principle, there's nothing that ties you to this interpretation other
than your ability to extract information out of your model. If you
can build models with steady states that take as given less rather
than more behavioral properties of a dynamic system, you're free to
try your hand.
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