PercussiveRussel t1_jd50td1 wrote on March 21, 2023 at 9:46 PM

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

Ah yes, this helps a lot. Brings back a lot of statphys memories too. Thank you very much.

In a way, a time averaged system could be described as a mixed-state density matrix I suppose, which is where my intuition comes back again. I always picture a single object as being in a pure state, but there are ways it doesn't have to be.

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.

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.

That is not me trying to say my intuition was right by the way, it wasn't.

LoyalSol t1_jd586m6 wrote on March 21, 2023 at 10:35 PM

>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.