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Why is it that the second law of thermodynamics in terms of entropy doesn't change at negative absolute temperatures? Has it been observed in experiment that if you add heat to a system with negative absolute temperature (which decreases its entropy), the entropy of the surroundings increase in a way that the change in the entropy of universe won't be negative?
Edit: Why am I asking this question: Since it is a "law", if it is to be true at negative temperatures as well as positive temperatures, what I said above must have been observed in experiment. Therefore one can prove that when two systems, one with negative temperature, and the other with positive are brought in contact, heat flows from the one with negative temperature to the one with positive temperature. On the other hand, if it has been observed in experiment that heat flows from a system with negative temperature to a system with positive temperature in contact with it, then one concludes that the second law is also true at negative temperatures. I want to know which one, maybe both, is an experimental fact. The second law of thermodynamics in terms of entropy true at negative temperatures, or Heat flows from a system with negative temperature to a system with positive temperature in contact with it.