Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature.

Suppose I say a body has temperature -2 K. Can I interpret it physically?

• I am a negative temperature "partisan" but it is important to mention that it is not everyone's cup of tea. The arxiv link can be found here. Commented Mar 16, 2014 at 21:50
• @gatsu's position is also reflected in a Physics SE post pre-dating the paper he links: physics.stackexchange.com/q/76145 Commented Mar 16, 2014 at 23:09

2 Answers

Negative temperatures are only defined for systems where there are a limited number of energy states. Consider rising the temperature of such a system, then as the temperature starts rising, particles begin to move into higher energy states, and as the temperature continues rising, the number of particles in the lower energy states and in the higher energy states approaches equality. (This is a consequence of the definition of temperature in statistical mechanics for systems with limited states.) If we add energy into these systems in the proper manner, we can create a system in which the number of particles in the higher energy states is bigger than the number of the lower ones. Our system is then characterised as having a negative temperature. Hence, "a substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature." (http://en.wikipedia.org/wiki/Negative_temperature)

In general, as one adds energy to a system with a negative temperature, its entropy decreases. On the other hand, if the same energy is added to a system with positive temperature then its entropy increases.

• The 2 paragraphs in this entry are almost verbatim the same as the fourth and second paragraphs, respectively, of the Wikipedia entry on negative temperature. I hope that's because you edited that article, but if it's not, you at least need to state where you got this information. Commented Mar 17, 2014 at 3:24

I think that the simplest way to wrap one's head around negative temperatures is that one: $$\beta = 1/T$$ The point is -- it is much more "physical" to describe a temperature of a body in terms of $\beta$. (We are using inverse of $\beta$ for a number of practical and historical reasons, but nevertheless.)

The larger that quantity $\beta$ -- the lower the temperature of a body. Notice that getting to absolute zero $T=0$ in that language means $\beta\to\infty$, making inaccessibility of it much more transparent.

On the other hand $\beta=0$ ($\Rightarrow T=\infty$) is not as restricted and you can go into negative values of $\beta$, thus getting negative (and very large) values of $T$.