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Luke_A_Somers comments on Entropy and Temperature - Less Wrong
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What gives a better intuition is thinking in inverse temperature.
Regular temperature is, 'how weakly is this thing trying to grab more energy so as to increase its entropy'.
Inverse temperature is 'how strongly...' and when that gets down to 0, it's natural to see it continue on into negatives, where it's trying to shed energy to increase its entropy.