Yes can actually set up some systems to a state that, theoretically speaking, has a negative temperature. This means that you would be more likely to find it in a state with higher energy than low energy. Curiously, if you allow the system to be in contact with the environment, you would find that its temperature would first fall to minus infinity, then jump to plus infinity, and eventually cool down to the same value as the environment. Therefore any negative temperature is actually hotter than any positive temperature.
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