<instructions>Your goal is to analyze the following comment and estimate how highly it will be upvoted by the Hacker News community.</instructions><comment><author>Xcelerate</author><text>I don&apos;t really like the misleading headline, although it seems as though the actual paper does it as well (&lt;a href=&quot;http://arxiv.org/abs/1211.0545&quot; rel=&quot;nofollow&quot;&gt;http://arxiv.org/abs/1211.0545&lt;/a&gt;).  Temperature is conventionally defined as the average kinetic energy of a collection of particles.&lt;p&gt;However, in statistical mechanics, you derive thermodynamic relations from the principles of quantum mechanics.  It turns out there is a term β which for most purposes seems to match up with 1/kT, where k is the Boltzmann constant and T is classical temperature.  According to this article, there are some occasions where &quot;conventional&quot; T and quantum mechanical T do not match up.&lt;p&gt;The most famous relationship in statistical mechanics is:&lt;p&gt;S = k ln Ω&lt;p&gt;S is entropy.  Ω is the partition function for the microcanonical ensemble, and it corresponds to the number of quantum states available to a system. (In English: Ω is the number of different configurations that a system of particles can possible have.)&lt;p&gt;Another relation that can be derived is:&lt;p&gt;1/kT = ∂ln(Ω)/ ∂E&lt;p&gt;Substituting the first equation into the second, we get&lt;p&gt;1/T = ∂S/∂E&lt;p&gt;So what would a negative temperature imply?  That increasing energy leads to decreasing entropy.  My guess is that these researchers have created some system that does exactly that.</text><parent_chain></parent_chain></comment><story><title>Quantum gas goes below absolute zero</title><url>http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146</url></story>
<instructions>Your goal is to analyze the following comment and estimate how highly it will be upvoted by the Hacker News community.</instructions><comment><author>jpdoctor</author><text>The usual explanation of such things:  T is not so important as 1/T.  So negative abs temp is achieved by going through +infinity temp and coming back via -infinity temp.&lt;p&gt;Note that this is only allowed in systems which have states that are bounded in energy.  The usual example is a laser:  When in inversion, its absolute temperature (of the electron population) is negative.</text><parent_chain></parent_chain></comment><story><title>Quantum gas goes below absolute zero</title><url>http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146</url></story>