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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/

Technically, you can associate a temperature to the velocity of the atom measured relative to the container, and therefore obtain a "temperature" for that atom. But a lot of concepts become quite strained when you reduce things to single atoms, and temperature is one of them. A single atom does not have a temperature in the normal sense.

To your initial question: the phases of matter are only defined for molecular or atomic collectives. Single molecules or atoms do not have a clearly defined phase of aggregation. Even for large molecular collectives it is not always clear whether they are solid, liquid, or gas. For example, on geologic time scales, even some "solids" can flow.

The phases of matter are more like convenience concepts. We use them to simplify discussions that would otherwise be complex. There's nothing fundamental about them. Do not get stuck in rigid categorizations there, because there's no point in doing that.

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What's a solid liquid?

So to be a bit careful about how we go about defining things. Yes entropy will still be directly tied to an ensemble in that it is directly related to the probability of an observation. Probability of course being tied to thousands of observations. But the key is that entropy can be observed in any type of probabilistic system and will very often behave the same way in a system with millions of atoms or a system of a single particle. It will just be tied to different averages such as the time average, spacial average, etc.

Where entropy is distinguished between many other bulk properties is that the later are often the result of thousands of atoms acting in unison where as entropy can be observed even in a single particle system. It's especially true when talking about quantum descriptions of molecules.

For a single particle the Jacobian of the principle coordinate is the entropy term.

Say for example you have a classical particle who is attracted to a single point by the equation

E(r) = 1/2 * k * (r-r0)^2

In this system we can simply write the Jacobian as a function of r. For an N-dimensional system

J(r) = r^(N-1)

Assuming we integrate the angular terms out. If you perform a simulation of the particle with a given momentum. One of the things of course in a system with conserved momentum is that while the lowest energy position is a distance from the center r0, the time average position will only be r0 if we perform the simulation in 1 dimension. If we have two dimensions you will notice the value will be some value above r0. And as we add more and more dimensions the particle will deviate more and more from r0 outwards. That is because as you increase the number of accessible dimensions you increase the translational entropy. A hyper-dimensional particle will spend very little time near r0 despite r0 being the most stable position.

You don't need multiple equivalent systems to observe this. The time average of a single particle will give rise to this.

In statistical mechanics and such we usually define these in terms of a number of equivalent systems because in practice that's what we are typically measuring and we take advantage of the ergodic hypothesis to link the time average to other averages of interest. But the thing about entropic effects is that they show up even in atomic and sub-atomic systems and many behaviors are a direct result of it. For example if an electron can be excited to a higher set of orbitals where all the orbital is the same energy and one orbital has more momentum numbers than another sub-orbital that orbital will be preferred simply because there's more combinations that suborbital has.

Larger systems have more degrees of entropy they can take advantage of such as swap entropy, rotational entropy, etc. but the rules and interpretations are still very much the same no matter if you got 1 million particules or just one. That's not always the case for other bulk properties. Sometimes the bulk properties are only observable in the limit of the average and not on a single particle.

> Like it becomes free Na and Cl just floating around in water right?

They aren't free, they're solvated—that is, they're stabilized through interactions with the surrounding solvent. This is why they don't immediately bond, so we can't remove this crucial aspect.

> One bit of nitpick. Entropy is still very well defined even at the atomic level. There's many different types of entropy, but they all are related to the same underlying concept.

Isn't it clear from the context that I'm referring to the thermodynamic entropy as applied to ensembles of molecules to determine the equilibrium bulk state?

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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Also tangentially related, an octopus brain is toroidal (donut shaped) and its guy passes right through the hole in the middle of it.

"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?

Aqueous just means that it’s dissolved in a liquid. Ionic things dissolved in a liquid get covered in water molecules because the water molecules are polar and the ions are charged. Non-ionic things dissolved in liquid are usually just polar and can form hydrogen bonds with the water molecules so that it looks like a single solution as opposed to when things don’t dissolve

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Additionally, the rapid onset of negative health outcomes was because individuals had been HIV positive for much longer than a clinical definition for HIV positivity was developed. Treatment has improved, but for the early days of the AIDS epidemic there were people who had HIV for years before there was an official diagnosis, so the rate of time from diagnosis to death/disabling symptoms appeared shorter. Now HIV testing is part of established STI screenings, so there's (on average) less time for the virus to inhabit a person before diagnosis.

Aqueous here means that the solution which constitutes a solvent and solute, has water as the chosen solvent.

Example being Sodium Chloride. Sodium Chloride (aq) simply means that you have a saline solution. The individual atoms of Sodium Chloride are dissolved in liquid water.

I wouldn't really call NaCl a liquid if you have NaCl (aq) because you're no longer dealing with pure NaCl. The aqueous solution is a liquid though.

This leads to an interesting question about solids that do not dissolve in a liquid. Here you're dealing with a type of colloid (effectively one phase suspended in another phase) And the dispersed compound does not have to be solid btw- it can be liquid (such as milk).

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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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What about Bose einstein condensate?

Semi-related question - when I took gen chem in college, if a solid was dissolved in a liquid it was always denoted as “aqueous” and we were told to treat it as a liquid, but it was never really clear to me whether that substance is a liquid or a solid. Can you explain the “aqueous” designation?

You also have to account for the issue that the first round of people getting Aids in the US and europe were largely part of the gay population at a time of extreme homophobia compounded by fear of this unknown disease. So - many were denied medical care or given extremely insufficient medical care, and the minimal treatments we had were delayed even further. Ie - if someone had the exact same disease today, without using any additional scientific breakthroughs or treatments from the last 50 years, just by not ostracizing the patient, you would see significantly better outcomes.

Then, there is the flip side that people would hide they had the disease as long as they could. Once they couldn't anymore, it was near the end - giving the impression of a sudden death after starting symptoms.

Only tangentially related, but the squid giant axon^TM is one of the largest (diameter) axons known. It's commonly used to study the affects of various drugs/conditions on action potential; initial work there led to a Nobel prize.

https://en.wikipedia.org/wiki/Squid_giant_axon