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KarlSethMoran t1_jd4fn4k wrote

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

It doesn't. You need internal degrees of freedom to define temperature. An isolated atom has zero internal degrees of freedom due to Galilean invariance.

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lizardweenie t1_jd4l91d wrote

An atom has internal degrees of freedom due to electronic and spin transitions, so it can certainly be excited. In general though as previous users mentioned, temperature is an ensemble property, so the atom wouldn't have a well defined temperature.

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Dr-Luemmler t1_jd7e31c wrote

An ensemble can also be one atom or one molecule. So yes, it certainly has a well defined temperature.

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lizardweenie t1_jd92qsl wrote

As other posters have mentioned, temperature is a property of a distribution. It tells us the probability of populating an excitation of a given energy. This isn't up for debate, it's just a matter of definitions. If you want to come up with some new concept that is well defined for a single particle, that's cool, but temperature doesn't work for single particles.

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Dr-Luemmler t1_jd9m4t4 wrote

Oh, the distribution works if there are multiple available states at a given energy level. And there are. You can even calculate it for a single particle in a box. We actually did in class...

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lizardweenie t1_jd9xip3 wrote

I don't mean to be rude, but it really seems like you haven't learned about temperature in a rigorous way (Like you would in a statistical mechanics class). It sounds like you've at least had some sort of exposure to undergrad level quantum mechanics, which is great. But recognize that your knowledge may not apply to this, and consider taking a statistical physics class.

If you did take such a class, you would learn that beta (which is propositional to 1/T) can be defined in terms of the partition function of the system of interest, but the entire concept relies on having multiple particles, (not simply one particle that transitions from state to state).

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Dr-Luemmler t1_jdaglj7 wrote

I dont want to be rude, but you just need different states the particle could be, which you get with the quatification of impulse for each direction and the electronic states. Having multiple undistinguishable particle, and measuring their states is just one way to calculate the partition function. Another one is to track the trajectory of a single particle. In other words, we just need different states with different probabilities. I see no reason why that would not hold for a single atom. Temperature itself is also not a relative measurement as you can also see temperature dependent radiation from only a single atom.

The temperature in thermodynamics is defined as $T = dE/dS$. As $S \approx log(\Omega)$, the amount of "accessible" states need to increase with increasing temperature to hold the first formula. As a single atom has three dofs, we fullfill it.

Sorry, I really see no reason you could be right. I have also studied a bit advanced statistical thermodynamics and wrote my BA in that field. But I can be wrong, I cant say I was excellent in that field and some years have past since then. Maybe you can give me some hints for proper literature.

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lizardweenie t1_jdamc26 wrote

No worries, you're not being rude. As for references, this a matter of basic definitions so I'd recommend some good textbooks, depending on your background.

I'd say that Chandler's book is pretty good: (I used it at the beginning of my PhD) http://pcossgroup.xmu.edu.cn/old/users/xlu/group/courses/apc/imsm_chandler.pdf

If you're looking for a different perspective, I've heard good things about Reichl: "A Modern Course in Statistical Physics"

Fun fact about this statement: > the amount of "accessible" states need to increase with increasing temperature to hold the first formula

This need not be the case. In certain scenarios, you can actually obtain negative temperatures which are perfectly valid. https://en.wikipedia.org/wiki/Negative_temperature

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lizardweenie t1_jdapyy8 wrote

I just thought of a reasonable thought experiment that might clarify your confusion:

Say you have a bath of non interacting hydrogen atoms (consider for a moment, only electronic excitation), and we are able to measure the state of each atom.

Say we measure this bath and find that f_0 fraction are in the ground electronic state E0, and f_1 are in the first excited state E1. We could then infer a temperature by comparing these populations to a Boltzmann distribution, which tells us the relative probability of finding an atom in a state at a given energy (for a given temperature). In this case temperature is a well defined and meaningful concept.

Now say instead that we have a single hydrogen atom, we measure its state, and we find that it's in the first excited state. What then is the temperature? If we try to infer a temperature from this, (using a Boltzmann distribution), we get -inf. Say instead we measure it, and it's in E0. In this case, our inferred temperature will be 0. So for this single atom system, any temperature that we try measure can only give two values, (0, or negative infinity). In this system, clearly temperature isn't behaving how we would like it to.

This troublesome result points to a larger problem with the question: asking "what is the probability distribution for state occupation" doesn't really work well for the example: the atom was measured and determined to be in state E1, its probability distribution is a delta function, which is an inherently non-thermal distribution.

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avoid3d t1_jd4urxm wrote

Hmm, in physics we learned that a more nuanced way of reasoning about temperature is relating it to the change in entropy as heat is added.

If I understand you correctly you are arguing that heat cannot be added to a single atom since there are no inter molecular forces to create oscillations to store the heat.

I’d argue that heat can be added since there are other kinds of energy states that are possible in a single atom such as electric phenomena.

Is there something I’m misunderstanding?

edit This lovely commenter explains this topic very well:

https://www.reddit.com/r/askscience/comments/11x4f9t/comment/jd4r58z/

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RevengencerAlf t1_jd4xdut wrote

I think this is both true and kind of not and it gets weirdly philosophical. It doesn't have temperature as we're taught about it in HS physics class, sure, since that is generally the internal kinetic energy of molecules vibrating and bumping into each other, but atoms themselves have internal degrees of freedom at the quantum level that can reasonably be used to describe temperature. The excitement state of an atom's electrons is the most obvious one.

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KarlSethMoran t1_jd4ys58 wrote

Sure. That is the electronic temperature. I was coming from the perspective of a classical point-particle picture and the kinetic, not thermodynamic, definition of temperature.

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MarzipanMission t1_jd520vi wrote

How is thermodynamic temperature different from viewing it from a kinetic perspective?

Does that mean that the movement of atoms relative to each other, in the kinetic sense of temperature, is not what the temperatures talk about in thermodynamics? So temperature is not a universal concept then? It is context dependent, and has many definitions?

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sticklebat t1_jd58ks6 wrote

Thermodynamic temperature is defined as the rate at which the internal energy of a system changes as its entropy changes.

In contrast, temperature from kinetic theory is essentially a measure of the average translational kinetic energy of the particles in a system.

The two are sometimes, but not typically, equal. The temperature that you know and love is the second one, but thermodynamic temperature is also widely used in science.

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wnoise t1_jd5kly2 wrote

The second is special case of the first. The statistical mechanics temperature really is the fundamental one.

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sticklebat t1_jd5ppqo wrote

Yep. But in most scenarios corresponding to human experience the first is reasonably applicable and much easier to understand.

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Dr-Luemmler t1_jd7c3ex wrote

>So temperature is not a universal concept then? It is context dependent, and has many definitions?

Yes it has, but the definitions are all different sides of the same coin. Or in other words, they add in complexity, but are more or less the same. They are not contradicting.

Temperature IS the average kinetic energy of a systems particles. Thats not just the classical definition that is also the result if you combine quantum theory and statistical thermodynamics. This kinetic energy just is not only translational but also rotation and vibration. A single atom though, does not have the degrees of freedom to rotate or vibrate. Besides its spin, but that is not important here.

There is another dof, and thats the electronic one. Yes, here energy can also be stored. Also probably neglectable here, but OP was very unprecise with his thought experiment here...

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glurth t1_jd4n4io wrote

"You need internal degrees of freedom to define temperature."

This sounds inaccurate. Wouldn't the excitement states of a single atom's electrons be an internal degree of freedom?

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KarlSethMoran t1_jd4x47b wrote

That would define the electronic temperature, not the temperature of the atom in the classical, point particle picture.

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Merakel t1_jd4oogr wrote

It sounds weird to me too, but I also at first thought he was talking about fahrenheit so I'm probably not worth listening to :/

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blacksideblue t1_jd52p3b wrote

so in a zero pressure environment like space, does that mean all matter is out of phase until gravity or some form of surface tension groups atoms together?

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KarlSethMoran t1_jd6vmwt wrote

I don't get what you mean by "out of phase". Gravity is exceedingly weak at the atomic scale, it can be safely ignored.

Atoms feel van der Waals attraction. It's a very weak interaction, but billions of billions times stronger than gravity at this scale still. It will get even noble gases into a crystal when there's sufficiently little motion.

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