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.)
Notice how there are locations in the EDFs shown above in which there are positive slopes. We don’t say that these plasmas (i.e. flouresant light bulbs) are negative temperature. We just state the obvious: these systems are not-in-thermal equilibrium.
So, the authors of the Science paper should not have stated that the temperature was negative in their system. They should have just stated that energy distribution function had a positive slope (like many other systems…including all laser systems.)
The problem was that this over-hype caused the science news agencies to go way over-board.
(1) Some of the news agencies suggested that there is a connection between EDF’s with positive slopes and dark energy. Making a connection between EDF's with negative slopes and "dark energy" is silly. Dark energy is related to the expansion of the universe. Making a connection between the two topics is like saying that understanding the EEDF of fluorescent light bulbs (or lasers) can provide insight into dark energy. I can think of no connection between EDF's with negative slopes and the expansion of the universe.
(2) Some of the news agencies suggested that we could use these systems with negative temperatures to generate even more electricity from power plants. This is an insane suggestion, and shows that the people working for these agencies have no fundamental understanding of the laws of thermodynamics. They have absolutely no clue how much electricity is consumed generating these ultra-cold systems (and even generating so-called negative energy systems.) It takes work to create system on Earth with temperatures less than Earth’s temperature. Even if you then use the low temperature system in the tail end of power plant system, you will end up spending more electricity creating the low temperature system than you will gain in extra-electricity at the power plant (compared with just using cooling water at the power plant.) Some of the news agencies suggested that the science described in the article could be used to improve power plants. This is just fundamentally incorrect. If you are interested in learning more about why this is impossible, then read more about the concept of exergy. The exergy of systems less than 300 K is positive, just as is the exergy of systems above 300 K. The exergy of system near zero Kelvin can be extremely large, which means that a lot of work went into creating it (i.e. more work went into creating it than you could possible generate additionally at a power plant.)
So, here’s a quick summary of the problems with the Science article that was picked up so many science news agencies.
(1) The slope of the energy population distribution function can be used to determine the temperature only if the system is in equilibrium.
(2) If a system is not in equilibrium, you can't use the slope of the energy distribution function to determine the temperature.
(3) For systems that are not in equilibrium, you must go back to an alternative definition of temperature.
This alternative definition of temperature is the following: the ratio of the total energy to the total entropy. Therefore, temperature can only be negative if either the total energy or the total entropy is negative. (And not both at the same time)
(4) But the total energy and the total entropy of a system are both positive quantities, which is why temperature is always positive.
(5) Therefore, the conclusions of the paper are incorrect. The authors are studying a really interesting non-equilibrium phenomenon, but they are not studying a system with negative temperature...just a system with a negative slope in the energy population distribution function.