Double Negative Kelvin

Reports that researchers elicited a temperature "lower than absolute zero" might make one question the meaning of the word absolute.  On Built on Facts, Matt Springer writes "temperature is a relationship between energy and entropy, and you can do some weird things to entropy and energy and get the formal definition of temperature to come out negative."  Usually collisions between atoms ensure that less than 50% of atoms in a sample are excited, no matter how much heat you add.  But Springer analogizes "What if I start with a huge pile of ground-state atoms, and one by one I whack them with a hammer to get them excited and then throw my collection of excited atoms into a jar?"  In this case, as more than 50% of the atoms are excited, physical equations yield a negative temperature.  Chad Orzel explains that the smallest negative temperature (i.e. -.01 K) reflects the highest concentration of excited atoms, while larger negative temperatures (i.e. -100K) actually approach lukewarm.  In his latest post, Chad Orzel breaks down the highly technical details of the researchers' accomplishment.