Is the idea of negative absolute temperature analogous to a virtual image?

AI Thread Summary
The discussion explores the analogy between negative absolute temperature and virtual images in geometrical optics. It highlights that temperature is defined by its relationship to entropy, suggesting that the reciprocal of temperature parallels the reciprocal relationships in optics, such as object distance and focal length. As real images transition to virtual images at positive infinity, a similar crossover is proposed for materials exhibiting negative temperatures. This mathematical behavior supports the comparison between the two concepts. The analogy presents an intriguing perspective on understanding negative absolute temperature.
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Is the idea of negative absolute temperature analogous to a virtual image in geometrical optics?

I was reading this article about such a negative temperature:

http://www.livescience.com/25959-atoms-colder-than-absolute-zero.html

It seems to me that since temperature is defined by its relationship to entropy, its reciprocal is the key expression. Similarly, the distance of an object, image or focal length in an optical system is related as per their reciprocals. The way it works is that as the distance of a real (i.e., positive-valued) image goes to positive infinity, it crosses over to negative infinity, at which time it changes from a real image to a virtual image. This seems to be the observed behavior, mathematically speaking, for this material having a negative temperature.
 
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That seems to me to be an eminently reasonable comparison.
 
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