I don't understand this, at least as it is explained here. Somebody
care
to explain?
Temperature is not (as we tend to think of it) a level, like the
level of water in a lake.
Instead, it measures how the total energy in a system is divided up
among its parts.
Statistically speaking, it's overwhelmingly likely that there's a
self-similar distribution of energies, with the ratio of higher
energy subsystems to lower constant.
This constant[0] is related to the temperature[1], and in normal
experience, it goes between absolute zero, where there is "no" energy
in the system and hence all subsystems are in their lowest energy
state, so there is no chance to find any higher states; and an
infinite temperature, where the energy in the system is evenly
divided between all possibilities and so it's equally likely to find
a higher energy subsystem as a lower.
If, however, one locally prepares a system so that there are more
higher energy subsystems than lower ones, the probability of getting
a higher-energy subsystem is higher than that of a lower, and,
because of the way we've defined temperature[1] the math works out
such that we see a *negative* temperature.
In fact, this is not "colder" than zero, it's "hotter"[2].
But it's not that unusual: the lasers in CD-players or laser pointers
(we are all old enough to remember these, right?) work because of a
population inversion[3], and anyone with a hydroelectric plant, or
for that matter a traditional dam-powered sawmill[4], also created
negative temperature situations.
-Dave
[0] it's possible to prepare systems that, strictly speaking, don't
have a "temperature" in this sense, because they have unusual
distributions; but one can usually come up with a "closest
temperature" to a given distribution.
[1] the inverse of the logarithm of the constant, more or less
[2] a very rough rule of thumb is that chemical reactions double
their speed with each 10 degree (C or K) increase in temperature,
because it's increasingly likely to find molecules with sufficient
activation energy (think of this as an "up-front cost" or "barrier to
entry") as temperature increases, and is why chemists are commonly
pictured with hot plates and bunsen burners.
[3] working lasers have a negative temperature component all the
frickin' time
[4] where locally there is more water above the turbine or grindstone
than below it, even though globally more water is in the oceans than
above...
