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.... if the model has the property being evaluated in a non-local
manner, or if it is not continuously extensive, then that property does
*not* flow for that particular model.
An example of such a model is for
a classical system of N classical Newtonian particles (e.g. a planetary
system or a galactic cluster) interacting via only their mutual
Newtonian gravitation.
For such a system the system's energy does *not* flow in any useful sense
of the word.
So, in a nutshell, whether or not energy flows depends on just what the
system is and how it is modeled.