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.