Negative temperatures do not exist

Scientists seeking publicity - move along now. Nothing worth seeing here. Move along now. : Image courtesy of LMU / MPQ Munich

Scientists seeking publicity – move along now. Nothing worth seeing here. Move along now. : Image courtesy of LMU / MPQ Munich

Some scientist aspire to belong to the ‘Impossible Things Before Breakfast’ (ITBB) Club. In my view, modern physics presents a pretty coherent and startlingly understandable picture of the world. For ITBB  club members this is anathema! For these iconoclasts, physics must always be paradoxical, requiring radical re-evaluation of everything we thought we ever knew. The latest applicants for ITBB club membership claim they have produced “negative temperatures”. This is nonsense.

  • Science Magazine Article Here (requires membership)
  • Live Science Report Here
  • Nature News Article Here

The temperature of a substance is a remarkable property. It is a single number that describes  the distribution of energies of particles within the substance on average. In a gas, the energy of the particles is held as kinetic energy of the molecules and so the temperature describes the distribution of molecular speeds. It describes this distribution in equilibrium. Those last two words mean something.

Even if you set up all the molecules initially with exactly the same speed, or any other distribution of speeds you care to create, once they have interacted with each other a few times – (crudely the interactions are described as “collisions”), their distribution of speeds will approximate a universal distribution, first predicted by James Clerk-Maxwell. The shape of the distribution is described by one single parameter – the temperature. And here is the amazing part – no matter how long the molecules continue to interact, this distribution of molecular speeds does not change. Wow! So temperature describes the distribution of molecular speeds in equilibrium.

If one could somehow take each molecule and instantaneously slow down the fast molecules and speed up the slow ones, then one could transiently describe the distribution of molecular speeds by a curve with a negative temperature. This is what the researchers have done – and its a great trick for which I congratulate them. However, they have not produced a gas with a negative temperature. As they themselves say:

Ulrich Schneider, a physicist at the University of Munich in Germany said “Yet the gas is not colder than zero kelvin, but hotter. It is even hotter than at any positive temperature — the temperature scale simply does not end at infinity, but jumps to negative values instead.”

I agree with Ulrich that the gas is not colder than absolute zero, but he is wrong when he says that the gas is hotter than any positive temperature. What he and his colleagues have produced is a gas which is not well described by any single number called temperature, because it is not in equilibrium

As soon as the molecules begin to interact, the distribution will tend towards the equilibrium distribution which would be described by a positive temperature – slightly higher than they started with. What happened was that the molecules were not in equilibrium with each other and that’s all. Nothing paradoxical, and nothing requiring radical re-assessment of thermodynamics. All that exists is a wanna-be member of the ITBB club seeking publicity and a flattering appearance on Horizon.

This concept is not even new. Non-equilbrium distributions of particle energies are routinely described with a negative temperature. And such distributions are created within the body of any material which supports laser action – so they exist inside every laser pointer. The key thing about these distributions are that they are not in equilibrium. They are not in any meaningful sense colder than absolute zero.

The work is very clever but it will not:

“…lead to new engines that could technically be more than 100 percent efficient, and shed light on mysteries such as dark energy, the mysterious substance that is apparently pulling our universe apart.”

Friends, we live in a beautiful and amazing world. And even more amazingly many aspects of it make some sort of sense – who would have expected that? While I sympathise with these researchers, who after months in their darkrooms emerge seeking the bright lights of fame and funding, it really doesn’t help anybody to make these nonsensical claims.

Move along now… nothing to see here…


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3 Responses to “Negative temperatures do not exist”

  1. Stephan Says:

    Happy new year Michael!

    Sorry but I think I disagree with you about negative temperatures. There are twopoints:
    1. You say the system is not in equilibrium. How did you arrive at this conclusion?
    2. Why would negative temperatures be plain impossible? There is no reason for that from classical theoretical thermodynamics.

    Unfortunately I don’t have access to the original article, but I read the news in Nature and the abstract in Science. Looks to me that they confined the atoms to a lattice with their magneto-optical traps (i.e. it’s a solid rather than gas) and then continue with temperatures of the spin system. From there on it looks like very much like work from the 90s in solid metals, which I have read in more detail at the time, for example Oja, Lounasmaa,

    You write “the energy of the particles is held as kinetic energy of the molecules”. I think this is not the case here, or definitely not in the work described by Oja and Lounasmaa. Even if they keep the atoms moving in the present work, the bulk of the energy is stored in the spins. This is “easily” achived by sufficiently large magnetic fields.

    Next you describe temperature as a parameter in the energy distribution of an ensemble in equilibrium. I totally agree, except for your using “molecular speeds” again instead of energies or microscopic states.

    Now what about the collisions or interactions? The particles may transfer kinetic energy when they collide. This does not change the overall energy distribution as long the kinetic energies are far lower than magnetic energies.
    Next, the particles may exchange spin alignment m_z. This is basically the only degree of freedom that you are left with. This kind of interaction makes the distribution go into an equilibrium. The collisions are dumb and know nothing of thermodynamics. The only thing they do is add a certain element of randomness and herefore primarily they add entropy without changind the total (free) energy. Once you are at the extremal entropy you are at equilibrium with a single parameter, temperature, describing the energy distribution. There is no need for this parameter to be positive. If your ensemble has a finite (m_z spin alignment values) rather than infinite number (as in kinetic energy) of available states, and a total energy that is more than N times the energy of the m_z = 0 state, then your only chance to maximise entropy (= reach equilibrium) is to have negative temperature. The maths is in the link above, if I remember correctly. If not, I may still have it written down somewhere. Anyway this is totally conventional, classical thermodynamics.
    Additionally, the entropy in the magnetic sub-system is by far higher than the entropy of motion in a magneto-optical trap or any decent 🙂 cryostat. I have done experiments with about 80% of the magnetic entropy removed, leaving you with about 0.1 kB per particle. The kinetic entropy of the solids in Oja/Lounasaa is
    many orders of magnitude smaller. (Another reason to disregard speed and motion).

    Finally, what about transferring energy from the spins to the atoms (kinetic energy)? The scales are so much different that this involves multi-particle interactions with correspondingly small probabilities. In the Oja/Lounasmaa (and subsequent) work the time scale for this process was in the range of weeks. That is longer than a typical thermos flask, and you wouldn’t say that you cannot measure temperature in a thermos flask because it is not in equilibrium, would you?

    So, the main point in this work is to have an isolated ensemble with a finite number of states. Interactions make the system go into equilibrium by maximising entropy according to conventional thermodynamics and in the end the distributioin will be the Maxwell-Boltzmann distribution with just one parameter, temperature. If you prepare the system accordingly, then the parameter “temperature” naturally turns out negative.

  2. protonsforbreakfast Says:

    Stephan in response to your comment:

    First of all, the paper is explicitly about creating a situation in which negative temperature applies to motional states – I think that’s what’s new about the paper. So I think I am correct in talking about molecular speeds.

    Regarding the question of equilibrium, as you say “The collisions are dumb and know nothing of thermodynamics.” So when high energy particles ‘collide’ low energy particles they will – as always – exchange energy and tend towards a standard distribution. So this distribution >cannot< be in equilibrium! Indeed the whole technique relies on the speed of switching and lasts for less than 1 second.
    Rough calculations indicate that within each lattice site the density is less than roughly 10^24 per cubic metre – I can’t say how much less – but it could be by a factor 10 or more. This gives a mean free path of roughly 1 lattice constant. At 1 nK the mean speed is roughly 0.8 mm/s or 1 lattice constant in 1 ms. So the atoms are in ‘Knudsen’-like state – hitting the walls of their containment cell rather than each other. Apologies for all the quasi-classical approximations involved in this estimate.

    Regarding the possibility of negative temperatures the authors also explicitly state that: “negative temperature states are hotter than positive energy states i.e. in thermal contact heat would flow from a negative to a positive temperature system”. My guess is that a referee told them to include this statement to try to avoid some of the nonsensical reporting.

    In this respect the fact that their experiment started so close to absolute zero is confusing. The implication is that they have somehow ‘slipped across the border.’ The implication of the reporting of this work is that they have achieved a temperature colder than absolute zero: my point is that they have not, and that such states are impossible. Describing these temperatures as ‘negative’ may be technically correct, but the fact that there is a negative number attached to the description of the state is a theoretical anomaly.

    All the best


  3. David Says:

    I agree with you Michael. Let me add that in a laser you only need to violate one assumption of thermodynamics to get to negative temperatures: the ensemble of atoms in a laser is in a (nonequilibrium) STEADY state. As long as a laser is switched on population inversion is maintained.

    In the optical lattice system not even that is true. The atoms in their experiment will eventually redistribute outwards due to the external potential. That might take a very long time (much longer than their experiment), but nevertheless the state is not even steady. I don’t understand all the hype about this work. They’re just using 1/T=dS/dE in a nonequilibrium system, but the equation is derived under the assumption of equilibrium between two subsystems.

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