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It is conventional to explain the heat capacity of the
structural materials in terms of "thermal phonons". Similarly
the main oscillatory motion of the oscillator is often called
"non-thermal". I'm not saying that's wrong, but I will say
it is not particularly fundamental.
The reason I say that is rooted in my experience. In my
line of work, it is likely that somebody will come to me
and ask what happens if we make a super-accurate measurement
of the pendulum, in some not-very-clock-like situation. At
some point, the uncertainty in the measurement will be dominated
by *thermal* noise in subsystem A. At this point *both*
subsystems are "thermal".