0 K is the coldest limit, and even that can never quite be reached.
You may have heard of negative temperatures, which can be (sort of) reached by spin systems, parts of lasers, and other materials if you ignore the electromagnetic modes. However, T < 0 does not correspond to things being colder than 0 K, but rather things being hotter
than any finite temperature. At ordinary T >0, the probability that a system can be found in a state falls off exponentially as a function of the state's energy. The higher T is, the slower that fall-off goes, so the more likely the system is to be in a high-energy state. For T < 0, the probability increases
exponentially with the state's energy. So that's like being hotter than hot.
(published on 07/04/2011)