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Maybe I dont get what you are saying about temperature, but what you are saying doesnt make sense to me. If a single atom wouldnt have a temperature, because it cant have a velocity alone, what happens if we drop a second atom in the void? Does now (kinetic) energy spawn from nothing? Besides that, temperature itself isnt relative as we have a true zero. Even if it is just theoretical.

Ehm, what? I know what you are saying, but just because you need some kind of interaction to measure ANYTHING. Or in other words with that logic you couldnt even measure the impuls of a flying particle because to measure it, the particle would need to interact with another particle somehow. In a simulation you for example could measure the energy level of a single particle and then determine its state. So here for md. For dft simulations you could also use the electron probability densities to determine the distance to other particles.

This kind of access to the physics are not availible for a single atom ofc

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Phases of matter are more than convenient classifications of multiple atoms.

Because of their states, they exhibit different physical properties including changes in electrical conductance.

No. Once you get down to that scale, our macroscopic concepts don't apply. Quantum physics is strange and unintuitive.

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Liquid salt to me makes me think of molten salt heated past it's melting temperature, which is very different than an aqueous solution.

Sorry, I don’t see how this helps the OP. It sounds like you’re talking about looking at the behavior and any transitions over a very long time rather than relying on the ergodic hypothesis and stat mech assumptions based on large N. OK, so now you’ve calculated what you consider the entropy. I don’t get how this allows the OP to classify the atom as a bulk solid, liquid, or gas when it’s a lone aqueous atom.

I want to say no, but relative to what? Say the jar is floating in space with no radiation hitting it and the hydrogen atom is just teleported into the jar so their relative speeds are zero at the start.

Depends. Is the glass moving?

Another issue is the energy of an atom doesn’t determine its temperature. Not exactly.

The high school definition of temperature as the average kinetic energy of the particles is merely an approximation appropriate only for gasses. Thusly the “ideal gas law”.

It’s better to think of temperature as a thermodynamic arrow. Heat flows from higher temperatures to lower ones. The rigorous definition of temperature is the inverse of the derivative of the entropy with respect to energy:

T = 1 / δS/δE

As you add more energy to a system, it gets more entropy, but because entropy is logarithmic it grows slower. So the derivative gets smaller. Thusly the temperature rises.

The flow of energy from high temperatures to low temperatures means that total entropy rises, because the system with lower temperature gains more entropy from the infinitesimal of energy. It’s how the universe obeys the second law of thermodynamics: Entropy always increases.

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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>Because when you say that entropy is tied to the probability of an observation, that really doesn't hold for an object in a superposition, since its multiplicity of states is just 1 (the superposition itself), which is where we do need to be careful I guess. I'd call it classical probabilistic, and avoid all confusion with quantum probabilistic.

It gets a little strange in quantum, but you still have entropy effects there. But yeah it gets kind of harry just because super positions themselves are already strange to behind with.

It's been a while since I focused on quantum stuff so I won't go too much into those since I'll probably get myself into trouble. :)

>So, to get more philosophical: It feels like there needs to be some sort of "outside influence" on a single particle for it to have entropy. Would you agree with this line of thinking? For some definition of outside influence.

It's easier to understand with an outside influence, but even in the situation of say a classical particle in a box where all points in the box are equally probable, the more dimensions you have the less likely you will observe a particle in the center of the box. Simply because there is more area toward the edge of a hyper-cube than in the center and this effect grows with dimensions.

I guess we could say the box is an outside influence, but I guess we wouldn't have a system without any constraints what so ever? I would have to think about that.

For an isolated particle the volume of the space it occupies is where it gets it's entropy from. Even for a quantum particle in a box the trend is also true, but just not uniform since you have a wave function. The odds of observing a particle near the center of the box goes to 0 as the number of dimensions increases. You're more likely to observe it near the edge in higher dimensions.

Which also a bit of trivia, is why the translational partition term is usually the only one in statistical mechanics that has a volume component. Because the other forms of entropy deal with internal degrees of freedom where as translational entropy is the space of the system.

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Temperature is a macroscopic value. It is a measure of the kinetic energy of a large collection of atoms or molecules. Individual atoms do not.

One other wrench to throw into this thesis is that phase of matter is actually determined by a combination of temperature and pressure. The pressure of a single atom is also not a meaningful metric.

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We discuss states of matter in terms of how a molecule interacts with its neighbors. If the solvent is a liquid (water in the case of aqueous solution), all interactions that you would care about are liquid like. In the case of a solid solution ie. bronze they would be solid-like.

The key reason we note it as being a solution rather than a liquid is to point out that the neighbors a molecule interacts with are the solvent, rather than molecules of the same type.

What if an astronaut comes across it in the vacuum of space?

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thanks all for your answers

How fast would that be? Being a single atom in a glass jar?