A lot of the major scientific news agencies have recently picked up an article recently written in Science that claims to have created a material with a “so-called” negative temperature. The authors of the paper have not created a system that violates the Second Law of Thermodynamics. (Though, many of the ‘science writers’ for Scientific American and New Scientist make it sound as if they have.) Worse, the authors of all of the magazine articles suggest that this research might be relevant to dark energy in the universe. The goal of this post is to refute the conclusion in this Science article and the speculation by the news agencies.
Here are links to articles written by the science news agencies: New Scientist Scientific American Science Daily
While there have been a lot of previous research papers that discuss the topic of negative temperatures, the problem is that we should only be using the word temperature to describe a system that is in thermal equilibrium. The term “temperature” is only really defined for systems that are in thermal equilibrium. A system of particles can be out-of-thermal equilibrium when the energy distribution function (EDF) is a not perfectly straight line (on a log-linear) scale with a negative slope. In thermal equilibrium, the EDF is a perfectly straight line, and the negative slope of the line is inversely proportional to temperature.
When a system of particles is out-of-thermal equilibrium, you can’t use a single variable to describe interactions (such as reaction rates); you have to plot the full EDF. There are some interesting examples of EDF’s in which there are locations in the EDF in which locally the slope of the EDF is positive, i.e. there are more particles at energy (E) than at energy (E-x), where E-x is some value less than E. Below are a couple of electron energy distribution functions from weakly ionized plasmas (i.e. fluorescent light bulbs.)