What energy is conserved or transformed when an atom or smaller particle reaches absolute zero?

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I understand that energy can not be created or destroyed, only transformed. I believe I understand that temperature is just kinetic energy expressed through vibrations so when a particle gets closer to absolute zero, where does it’s energy go? Is it transformed into potential energy or something else?

In: Physics
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There is nothing special about the thermal energy as it approaches 0K, it’ll follow the same mechanisms of heat transfer as that at ambient temperatures, namely: conduction, convection and radiation.

Conduction and convection both operate by transferring thermal energy to another body, gaseous, liquid or solid. Energy is not transformed but imparted.

Radiation is a transformation of that thermal energy however, in which its expressed as EM radiation.

The only way for something to approach 0K is for the system to already be colder than it, so it can release its thermal energy

I think you’re mistaking an end state for a process.
IE, Your question is like asking “You are in Chicago, how did you get there?”

There might be any number of means to transfer out energy or transform it into potential energy. The end result of doing it effectively enough is that you reach absolute zero.
Note that science hasn’t figured this out yet, we’ve only just gotten really really close.