There are very specific conditions to allow this physics: It works only for extremely high temperatures, when the thermal energy is much greater than the spacing between energy levels. It's been known for a while that high energy physics deviates from the low energy cases of spacetime: One of the things though you have mentioned, ''is fully justified by the derived formula for <H> shown below that. Note it goes to precisely zero when T goes to zero.'' I have read many science articles in my time and I have seen authors talk about temperatures go to zero. This is never the case. I can assure you, there is no case in wikipedia that will allow a system to go to precisely zero. It's very badly written just glancing over the material. Just read the first bit carefully: ''At high temperatures, when the thermal energy kBT is much greater than the spacing hν between energy levels, the exponential argument βhν is much less than one and the average energy becomes kBT'' You see that? Average energy becomes k_B T!! That is, the energy becomes a more general explanation of k_BT, kinetic energy is still related to the thermal properties of the system!! You haven't disproven what I said, because you haven't taken either the physics properly into consideration or you didn't understand what you have read. This in no way disproves my claim that thermal properties of a system is linked to the motion of particles therein. Another thing, let's be clear, when you read something like this: ''However, at low temperatures, when hν >> kBT, the average energy goes to zero'' is an approximation near zero kelvin, a system never actually reaches it. Again, by a mixture of bad writing and unclear physics, I won't hold you fully to blame for any ignorance.