A thought experiment where a cup of some substance manages to be observed at a stable negative temperature.
This substance is a liquid at its current temperature. But it is colder than the ambient temperature of the room. As the liquid warms up from the ambient room temperature, it freezes. But taken outside on a cold day, it will melt and then evaporate?
I know you're not going to get a cup of this stuff in reality, but am I at least understanding the idea? The "temperature" of the liquid would remain negative, it's not like it could ever "warm up" to the point it was positive? It could reach an equilibrium state with its environment, but it would still be negative?
Yes, that's the right idea (assuming it has lower entropy when it's frozen than when it's liquid). In the context of the liquid you describe, and assuming it has otherwise normal properties then yes you can't warm it up (= add energy) and make it positive again. And if you took it outside, the temperature would first become more and more negative and then flip to positive. However, as long as we are talking about exotic stuff it is conceivable that as you add energy, the entropy first decreases (i.e. negative temperature) but if you add more and more energy, the entropy starts to go up again. For example lets say that if you add a lot of energy to the frozen stuff, it becomes a gas. I'm not sure if a system like that where you go from positive to negative to positive is physically possible, but I don't currently see any reason why it wouldn't be.
An object with negative temperature is hotter than an object with positive temperature. So it's not possible for the cup of negative temperature liquid to be "cooler" than the ambient temperature of the room. The liquid's temperature will get more and more negative until it flips from negative infinity to positive infinity, and then cool down from there until it equilibrates with the ambient environment.
A thought experiment where a cup of some substance manages to be observed at a stable negative temperature.
This substance is a liquid at its current temperature. But it is colder than the ambient temperature of the room. As the liquid warms up from the ambient room temperature, it freezes. But taken outside on a cold day, it will melt and then evaporate?
I know you're not going to get a cup of this stuff in reality, but am I at least understanding the idea? The "temperature" of the liquid would remain negative, it's not like it could ever "warm up" to the point it was positive? It could reach an equilibrium state with its environment, but it would still be negative?