Phonon energy and atomic vibration energy

[camilo]

When we say that a phonon vibration mode has an average energy <E> are we saying that all atoms (or harmonic oscillators) in a piece of matter (eg. a nanoparticle) will also has that energy, or that the piece of matter as a whole will have that energy ?
In the second case the amplitude of the oscillations of the atoms will be lower the bigger the piece of matter, for a constant <E>, I guess.

Thank you.

 

[DrDu]

The second option is correct and also your conclusion.