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by sampo 4338 days ago
It depends on what we mean by "temperature".

If we think that temperature is a measure of how much the atoms move around then it is not possible to have less than zero movement.

But if we think temperature as related to the ratio of how much a system's entropy changes when a certain amount of energy is added (or removed) to the system [1],

1/T = dS/dq

then it's possible to construct systems with a negative T.

[1] Eqs. 8–10 in http://en.wikipedia.org/wiki/Temperature#Second_law_of_therm...
1 comments
simias 4337 days ago
If I understand correctly, it's like saying a car has negative speed because it's going backwards. If you accelerate it forwards you actually reduce its speed towards 0, but that does not mean that the car is more immobile at -5km/h than at 0km/h.

It's just a matter of convention, a negative temperature just means that the temperature gets closer to 0 as you add energy. Did I get that correctly?

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mjfl 4337 days ago
Negative temperature actually has some nuance to it. By the relation 1/T = dS/dq where T is temperature, S is entropy and q is heat added to the system, a negative temperature means that entropy decreases when you add heat to the system and increases when it emits heat. By the second law, entropy always goes up, so a negative temperature object will always emit heat. In that way, something with a negative temperature is extremely hot.
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AnimalMuppet 4337 days ago
In fact, it's a negative absolute temperature because it's hotter than infinity.
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sampo 4337 days ago
> If I understand correctly, it's like saying a car has negative speed because it's going backwards.

Well, kind of, but I think that would be an oversimplification.

Negative temperatures have a concrete physical meaning, being "hotter than infinity", in the sense that if we bring in contact 2 systems: one with an arbitrarily high positive temperature, and one with a negative temperature, energy (heat) will flow from the negative system to the positive.

This looks tidier if we use the thermodynamic beta (beta = 1/T) instead of temperature. Then we can say that heat always flows from a system with a smaller beta to systems with a larger beta.

http://en.wikipedia.org/wiki/Thermodynamic_beta

Maybe debt is a somewhat useful metaphor here. If someone has a debt of 5 apples, in some ways if makes sense to say that this person owns -5 apples. But in some other ways it makes no sense: a person with 5 apples can eat them to get less hungry. A person with -5 apples cannot eat them to get more hungry.

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