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florinandrei t1_jd6bwq6 wrote

Reply to comment by Dr-Luemmler in Can a single atom be determined to be in any particular phase of matter? by Zalack

It definitely does have a kinetic energy.

The only thing is - when you go from kinetic energy to temperature, you run into all sorts of trouble if you do it for single entities.

Temperature is an inherently collective measure. If it's single particles, stick to kinetic energy.

What is the "temperature" of this marble I'm throwing? ;) (not the temperature of the glass, but the "temperature" of the marble as a single particle with some kinetic energy)

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Dr-Luemmler t1_jd75stk wrote

Defining temperature by kinetic energy, you could calculate it for a single marble. If you want to use the advanced definition of temperature via entropy, sure lets do it:

$T = dE/dS $

So temperature is the change of internal energy when changing the entropy. In statistical thermodynamics, one can now define entropy by the number of availible states $\Omega$ with its degrees of freedom.

The degrees of freedom a single atom has are $3N-3$ = 0. That basically means, this atom only has the translation dofs and the electronic ones. Lets neglect the electronic ones (even though they might be important, as with then we might be able to measure the temperature) then the temperature of a single atom is solely defined by its kinetic energy.

Can we access it in labratory without using the interaction with other atoms? No! But in simulations we can. Or what kinds of problems do we have?

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