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Does it make sense to ask 'what is the temperature of an atom?'. Why not?

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Systems in equilibrium have the energy of their atoms described by the Boltzmann distribution (https://en.m.wikipedia.org/wiki/Boltzmann_distribution)

$p_i \propto e^{\frac{E_i}{k_BT}}$

$p_i$ is the probability of finding an atom in state $i$

$E_i$ is the energy of state $i$

$k_B$ is the Boltzmann constant

$T$ is the temperature

Like most other probability distributions, you can calculate averages using them, and in this case the average kinetic energy of the atoms is proportional to the temperature.

Given the above it's fair to say that it is at the very least confusing to talk about the temperature of an individual atom. However, if someone were to say this, I would suspect they would mean that the atom has the same energy as the average energy of a collection of atoms at that temperature. Or stated more simply/mathematically, the energy of the atom is $k_BT$.

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