Another odd consequence of negative temperatures has to do with entropy, which is a measure of how disorderly a system is. When objects with positive temperature release energy, they increase the entropy of things around them, making them behave more chaotically. However, when objects with negative temperatures release energy, they can actually absorb entropy.
Negative temperatures would be thought impossible, since there is typically no upper bound for how much energy atoms can have, as far as theory currently suggests. (There is a limit to what speed they can travel — according to Einstein's theory of relativity, nothing can accelerate to speeds faster than light.)