It's a negative on negative absolute temperatures

December 20, 2013 by Jennifer Chu
A 1660 wood engraving of Robert Fludd's 1618 "water screw" perpetual motion machine, widely credited as the first recorded attempt to describe such a device for useful work. Credit: George A. Bockler

The concept of a perpetual motion machine is an enticing one: Imagine a machine that runs continuously without requiring any external energy—a feat that could make refueling vehicles a thing of the past.

While a machine inspires appealing possibilities, most scientists agree that such a machine is impossible, as the very concept—doing work without any energy input—defies the laws of thermodynamics. Nevertheless, some researchers have forged ahead with efforts to create systems resembling perpetual motion at microscopic scales, including spin systems and ultracold quantum gas, which have suggested that perpetual motion machines may be more than pie-in-the-sky notions.

But now, mathematicians at MIT and the Max Planck Institute for Astrophysics have challenged these ideas with equations showing that such systems, while innovative, do not illustrate the dynamics of perpetual motion. The main claim of such experiments is that they are able to produce systems with negative absolute temperatures, or temperatures below 0 degrees Kelvin. If true, such systems could be used to build machines that produce more work than the heat energy put into them—a key characteristic of perpetual motion.

In a paper published this month in the journal Nature Physics, the researchers analyzed past claims of negative absolute temperature and found that in all cases, scientists were interpreting experiments based on a flawed—though universally accepted—definition of entropy, or heat. This definition, called the Boltzmann entropy, appears in modern physics textbooks, and is widely used to calculate the absolute temperature of a wide range of physical systems.

But as the MIT team found, the definition only works when atomic or molecular energy states exhibit a normal distribution, where higher energy levels are less frequently populated than lower ones. In more exotic systems, such as certain quantum gases, the definition breaks down. Accounting for this error, the team performed mathematical consistency checks using an earlier definition of entropy, and found that such systems actually exhibited positive absolute temperatures—a result suggesting that previous studies were using the wrong definition, or essentially an inaccurate theoretical "thermometer," to measure the absolute temperature of exotic systems.

"It's sad in a sense, because you want something to be spectacular, and you want to find something new," says Jörn Dunkel, an assistant professor of mathematics at MIT. "But it's good, in a way, because the implications of negative absolute temperatures would have shaken up the foundations of physics."

The case for going below absolute zero

We typically think of temperature as measured in degrees Celsius or Fahrenheit, which can reach subzero temperatures. In contrast, absolute temperature, measured along the Kelvin scale, represents the motion of molecules within a system. At absolute zero, molecules stop moving, and the system cannot get any colder.

Interestingly, the concept of negative absolute temperature doesn't imply that a system is colder than absolute zero, but in fact, much, much hotter. Systems above typically exhibit a normal energy distribution in which there are more atoms or molecules in lower than higher energy states.

Under very special conditions, it is possible to flip-flop, or invert, such energy distributions. A well-known example is the laser, which relies on the fact that the majority of its electrons occupy high-energy states. Applying Boltzmann's definition of entropy in these situations yields a negative temperature. If one inserts such negative temperatures into an equation for the efficiency of a heat engine, known as Carnot's formula, then one can obtain efficiency values larger than 1—predicting, in effect, perpetual motion.

Rewriting the textbooks

To check whether past claims of negative absolute temperatures were indeed correct, Dunkel and Stefan Hilbert, a postdoc at the Max Planck Institute, methodically examined the equations used in earlier studies to calculate absolute temperature. They found that, while the Boltzmann definition of entropy works well in calculating positive absolute temperature, it quickly falls apart when used to find the temperature of systems with an inverted distribution of molecules.

Going further back in the literature of thermodynamics, the researchers reviewed another definition of entropy described by physicist J. Willard Gibbs in the early 20th century. As it turns out, the absolute temperatures derived using both the Gibbs and Boltzmann definitions for entropy are nearly identical for classical systems with a normal molecular distribution. But for more exotic systems with an inverted distribution, results from the two equations diverge greatly.

Dunkel and Hilbert performed mathematical checks and found that, using the Gibbs equation, they calculated positive absolute temperatures in inverted systems that scientists had thought were negative. The group's new calculations are consistent with the laws of thermodynamics and agree with standard measurement conventions for pressure and other thermodynamic variables, showing that while a system may exhibit an inverted distribution of atomic or molecular energies, this abnormal spread doesn't necessarily signal negative absolute temperatures.

Dunkel suggests that going forward, any researchers seeking to accurately measure the absolute temperature of exotic systems such as quantum gases should use Gibbs' formula over Boltzmann's.

"There are only a small number of textbooks that teach [Gibbs'] formula," Dunkel says. "They don't discuss negative temperatures, because at the time, it wasn't really relevant. But then [the formula] got lost at some point, and now all the modern textbooks publish the other formula. To correct that will be difficult."

Peter Hanggi, a professor of physics at the University of Augsburg, says the paper's findings will help scientists make much more accurate interpretations of rare, exotic systems.

"There were a lot of things being claimed and repeated in the general literature over 50 years, and this group has done an excellent job in sorting out the incorrect from the correct," says Hanggi, who was not involved in the research. "The main significance is to point out to everybody, 'Hey, wait a minute, if you calculate temperature, what does it mean for thermodynamics and for the experiment?' One cannot be too quick in their calculations."

As for creating a perpetual motion machine, Dunkel says the possibility is slim at best, and will require very careful calculations to verify.

"If you create a new class of systems, that's a huge experimental feat," Dunkel says. "But if you go on and interpret the things you measure on these systems, you need to be really careful. If you make just a small mistake in your assumptions, it can amplify hugely."

Explore further: Atoms at negative absolute temperature: The hottest systems in the world

More information: Consistent thermostatistics forbids negative absolute temperatures, Nature Physics (2013) DOI: 10.1038/nphys2815

Related Stories

Researchers force a gas to a temperature below absolute zero

January 4, 2013

(—A team of physicists in Germany have succeeded in forcing a gas to become colder than absolute zero. Using lasers and a magnetic field to manipulate an ultra-cold gas, the researchers, as they describe in their ...

Indecisive quanta

February 27, 2013

(—In ytterbium nickel phosphide there is a quantum critical point between the ferromagnetic and non-magnetic states that was previously not thought possible.

Recommended for you

Possible case for fifth force of nature

May 26, 2016

A team of physicists at the University of California has uploaded a paper to the arXiv preprint server in which they suggest that work done by a team in Hungary last year might have revealed the existence of a fifth force ...

Doubling down on Schrödinger's cat

May 26, 2016

Yale physicists have given Schrödinger's famous cat a second box to play in, and the result may help further the quest for reliable quantum computing.

Optics breakthrough to revamp night vision

May 24, 2016

A breakthrough by an Australian collaboration of researchers could make infra-red technology easy-to-use and cheap, potentially saving millions of dollars in defense and other areas using sensing devices, and boosting applications ...


Adjust slider to filter visible comments by rank

Display comments: newest first

1.6 / 5 (22) Dec 20, 2013
Still trying to retroactively close the door on the hundreds of over unity devices that are appearing all over the net, are we?

Too bad, too many of them, this time it will get out.

So, to stick with the pragmatic, nothing to see there, everyone go home! The closed loop of controlled science remains intact. Or at least the attempt to close it remains intact.

Except for one problem.

Time is unidirectional, and that breaks the closed loop. Whoops! Even Maxwell told you this, when he illustrated the very slight uni-directionality in the systems, and their inherent elasticity. That was a tough one to close, took some effort, eh? Gotta symmetrizing that thing before people start thinking, so get in there and help 'simplify' Maxwell's math. Right, right.

Every branch of science and physics is saying the same thing, that it is a false a glass ceiling and it is shattering.
1 / 5 (12) Dec 20, 2013
Our universe began apparently in a highly ordered state. Naturally it will probably adopt other, more scattered states. Yet something made the original highly ordered state. That mechanism is therefore viable. That negentropic mechanism is what most scientists refuse to investigate

Quantum entanglement, better known as gravity, is such a negentropic force and very poorly underdtood
4.8 / 5 (20) Dec 20, 2013
@KBK: I'm sorry that the laws of thermodynamics hurt your feelings.
5 / 5 (15) Dec 20, 2013
I'm pretty sure you can get perpetual motion machines using supercritical unicorn farts. I read it on the internet!
4.2 / 5 (9) Dec 20, 2013
@KBK: I'm sorry that the laws of thermodynamics hurt your feelings.

..........but hey KBK, don't become overly concerned about these believers in Asymptotic Pseudo-tensors who already are casting their one star votes in favor of "perpetual motion", they will always outnumber those of us who have taken the Thermodynamics courses, taken the final exam & gotten a real final passing grade.

The Asymptotic Pseudo-tensor crowd believes there is one kind of "entropy" for earth based energy systems & another kind of "entropy" for cosmology systems operating beyond the limits of our planet Earth & its solar system. You of course will know them by the one star votes they cast while never using the same name to post what exactly it is that makes them such intellectual giants.

Wait'll you see the one star votes this post by a nuclear/electrical engineer will get.
3 / 5 (4) Dec 20, 2013
That water screw device would have worked but the proper lube hadn't been invented yet.

BTW energy from the vacuum IS energy input. Scientists are just beginning to figure out how to get it to do useful work. The Casimir effect is one with potential.
3 / 5 (4) Dec 20, 2013
Casimir force "On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors... it is significant in some aspects of emerging microtechnologies and nanotechnologies."
not rated yet Dec 20, 2013
Absolute zero merely represents the point when the atoms have no "kinetic" energy.
1 / 5 (1) Dec 20, 2013
Who spoke about "the" definition of entropy? Please, have a read: Challenges to the Second Law of Thermodynamics:
3.7 / 5 (3) Dec 20, 2013
@KBK: I'm sorry that the laws of thermodynamics hurt your feelings.

..........but hey KBK, don't become overly concerned about these believers in Asymptotic Pseudo-tensors who already are casting their one star votes in favor of "perpetual motion", they will always outnumber those of us who have taken the Thermodynamics courses, taken the final exam & gotten a real final passing grade.
I studied thermodynamics. I also took a security on the WTC collapse caused by Arab goatherders living in a Pakistanian cave, which goes unchallenged by many scientists The Boltzmann distribution is now found to be wanting in this very article, yet it was a "law" until yesterday. I didn't see your post complaining yesterday about it. What is your point?
Dec 20, 2013
This comment has been removed by a moderator.
2.3 / 5 (3) Dec 20, 2013
But on to the topic of the article, so are you saying that there is no such thing as a perpetual motion machine? I thought there was a science rule that says they are impossible. But I might be confused about that. Do you know the name of that rule so I can put it in the google?

Look into "Heat Engine Cycle". It explains how entropy functions inside closed systems. After you understand why entropy can occur only inside a "closed system", you will better understand why such closed systems work even when we send rockets to the moon or Mars, thus negating the "open universe" concept in cosmology, could also be considered as "perpetual motion".

A heat engine cycle that is suddenly interrupted by a breach in the constraining cavity will cease to do work or will in very short order begin to operate very inefficiently. How quickly the energy cycle is affected depends on the cross sectional area of the breach as compared to the overall surface area of the constraining cavity.
2.3 / 5 (3) Dec 20, 2013
cont'd from previous.......When you look at the bell shaped model of the "open universe" model it is plain to see that the breach in the cavity of the system has a cross sectional area that is usually depicted in graphics to be as much as 25% of the total cross sectional area.

Try operating an internal combustion engine with 25% of the constraining cavity wall blown away & see how far that gets you, yet this is the silly model the "open universe" advocates would have us believe in, in other words "perpetual motion".
Dec 20, 2013
This comment has been removed by a moderator.
Whydening Gyre
5 / 5 (3) Dec 21, 2013
I get it now. Zeph fan is a marketing guy at Google...
5 / 5 (2) Dec 21, 2013
Perpetual motion, alchemy, squaring the circle, angels on the head of a pin, etc. = perpetual pseudoscience mental masturbation.
Dec 21, 2013
This comment has been removed by a moderator.
not rated yet Dec 23, 2013
wow... this universe deserves to die of heat death.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.