I think that unless you found the Unifying theory and the source for infinite energy, your phenomena stops at the electron motility levels.
Take potential wells/barriers, in a Josephson junction for example (Which has a boundary condition that violently disagrees with most of the basic principles of system equilibrium) there's a measurable current output as temperature lowers even when there's no potential difference across the electrodes, but it's because both superconductors having different ranges need to maintain phase coherency at the barrier.
In semiconductive materials the electrons need to have enough energy to traverse the potential barrier, so yes, once your energy is below that barrier you are done,a dn if you lower the temperature the material becomes less conductive.
In non-conductive material the potential barrier is much higher, your electrons must have a very high enery level to traverse the barrier or be exited with a tremendous amount of energy.
All materials have potential wells and barriers, some are lower than others.
Now in your impulse response dilemma, the energy of the impulse will eventually fall below the potential barrier of the material, the result? No more contributions to the material's movement and the response.
On resonances... all atoms resonate, not all molecules resonate (And some who resonate change states after resonation), why do you think that is happening?
I read Paul's posts, I don't see the ardent part... he's arguing this:
We have experimentally concluded that within observable intervals the energy decreases exponentially, ergo the energy in the system decreases exponentially and thus never approaches equilibrium.
That's the conclusion out of observable phenomena, what happens where we can't measure we can only infer with a mathematical model.
Again, what we know of the system is that it approaches a state where the phenomena is unobservable and it resembles the original state.
I'm not saying that the model is wrong, it's a model, but the model doesn't return to equilibrium, and that's a modellic assumption.
Say you want to make the model more complex, add all the forces, mechanical and electric, that affect your system, add losses, add leakage, add feedback and add random variations on those forces, does it mean that the observation of exponential loss is valid? Only on those intervals where it is observable and quantifiable... where you can't measure you can only infer.