# A System So Cold It's Hot

Scientists describe a physical system that is both below “absolute zero” and above “absolute hot” at the same time.
Image
Media credits

Myriams-Fotos via Pixabay

Media rights

CC0 Creative Commons

Yuen Yiu, Staff Writer

(Inside Science) -- Can temperature drop below absolute zero? What happens then? Does it pop out at the other end of the thermometer like Pac-Man and become infinitely hot? Well, kind of, and the seemingly wacky concept is actually surprisingly common in physics.

A recent paper published in Physical Review Letters describes a system where negative temperature is used to explain a weird but real phenomenon in our physical world.

But before you can understand how temperatures can be turned upside down, you'll need to relearn the meaning of temperature.

### Negative temperature is hotter than hot

Most people probably learned in school that temperature is basically just a measurement of how vigorously particles in a system shake: A high temperature means lots of shaking, and absolute zero means absolutely no shaking. While this interpretation may work to understand the temperature in your oven, it’s not the whole picture.

For a start, temperature isn't simply the average energy of all the particles in a system. It is actually related to the distribution of those energies. Imagine particles as bricks in a building, with the height of each brick reflecting each particle's energy. At low temperatures, the building looks similar to a pyramid that is short and fat at the bottom. At higher temperatures, the pyramid grows taller and skinnier. This trend continues as the temperature rises, up to what's known as the "absolute high" temperature -- where the pyramid transforms into a single column, stretching from the ground infinitely up toward the sky. This is where things begin to get weird.

If you can somehow push the system one step beyond “absolute high,” the pyramid shape suddenly reemerges, but this time it’s flipped -- each layer now contains more bricks than the one underneath it, with infinitely many bricks at the infinitely tall top. Here comes the even weirder part -- when this happens, the "temperature" in the equation describing the shape of this “pyramid” actually becomes negative.

An ever-expanding and infinitely tall upside-down pyramid may sound too ludicrous to even think about. Ditto for a negative temperature that is somehow hotter than infinite. But if we stop thinking of the particles’ energies as boundless kinetic energies, negative temperature is actually a very real parameter that can be used to describe the distribution of other kinds of energies inside a physical system.

"This is not necessarily the temperature in the classical sense -- there is a distinction between the different ways temperature is used to measure the properties of a system," said Stefan Hilbert, a physicist from Ludwig Maximilian University of Munich in Germany not involved in the paper. "For example, you can have a system with this so-called 'population inversion' -- where there are more parts of the system in an excited state than in a lower energy state."

In other words, physical systems that somehow limit the "pyramid" to a finite number of levels can actually be inverted. To see this mechanism at work, look no further than the unassuming laser pointer.

### Real world applications for an out-of-this-world concept

Every time you click on a laser pointer, you tap into the magic of "population inversion." Atoms are "pumped" from a lower energy level to a higher energy level, and then they fall back down, emitting light in the process.

Today, scientists are findings ways to manipulate other excitable physical systems. Spin -- the entity that determines the magnetic properties of an atom -- is among the hottest topics in negative temperature research.

"Before lasers, people thought if you have a bunch of spins you cannot excite more than half of them because that is [the] hottest possible state," said Kae Nemoto, a researcher from the National Institute of Informatics in Tokyo and an author of the paper.

But scientists have since shown that’s not true. In their paper, Nemoto and her colleagues describe a specific way to set up a spin system such that a part of its population actually prefers to be as inverted as possible. In other words, unlike lasers, where one needs to constantly "pump" atoms into the higher level, parts of their spin system actually flow upward naturally.

"[In lasers], there's a population inversion, but it's not really a steady state. You can populate the excited state, but the atoms are not gonna stay there for a long, long time," said William Munro, a researcher from the Nippon Telegraph and Telephone Corporation and another author on the paper.

Nemoto, Munro, and their colleague Yusuke Hama from the RIKEN Center for Emergent Matter Science in Saitama, Japan, discovered that if there are two separate pockets of atoms with spins sharing a reservoir with a fixed temperature, the two pockets don't necessarily reach an equilibrium in the end.

When the two pockets are equal in size, even when one started with all the spins in the higher state, and the other one all in the lower state, over time, both pockets end up in the middle, with half of the spins in the higher state, and half in the lower.

But something peculiar happens when the two pockets are different sizes. For example, if Pocket A contains more spins than Pocket B, while all the spins in Pocket A are in the higher state and all the spins in Pocket B are in the lower state, then the two do not both relax towards the lowest possible state like that of a laser. Instead, all the spins in Pocket B would flow towards the higher state. In other words, Pocket B actually prefers to be in the most inverted state possible. This revelation can guide future efforts to manipulate the magnetic systems that are ubiquitous in modern day applications.

"The idea of negative temperatures is important for interpreting the experimental results of many physical systems, especially for these spin systems, " said Hilbert.

Filed under
Author Bio & Story Archive

#### Yuen Yiu

Yuen Yiu is a former staff writer for Inside Science. He's a Ph.D. physicist and fluent in Cantonese and Mandarin. Follow Yuen on Twitter: @fromyiutoyou.

# A System So Cold It's Hot

Scientists describe a physical system that is both below “absolute zero” and above “absolute hot” at the same time.
Image
Media credits

Myriams-Fotos via Pixabay

Media rights

CC0 Creative Commons

Yuen Yiu, Staff Writer

(Inside Science) -- Can temperature drop below absolute zero? What happens then? Does it pop out at the other end of the thermometer like Pac-Man and become infinitely hot? Well, kind of, and the seemingly wacky concept is actually surprisingly common in physics.

A recent paper published in Physical Review Letters describes a system where negative temperature is used to explain a weird but real phenomenon in our physical world.

But before you can understand how temperatures can be turned upside down, you'll need to relearn the meaning of temperature.

### Negative temperature is hotter than hot

Most people probably learned in school that temperature is basically just a measurement of how vigorously particles in a system shake: A high temperature means lots of shaking, and absolute zero means absolutely no shaking. While this interpretation may work to understand the temperature in your oven, it’s not the whole picture.

For a start, temperature isn't simply the average energy of all the particles in a system. It is actually related to the distribution of those energies. Imagine particles as bricks in a building, with the height of each brick reflecting each particle's energy. At low temperatures, the building looks similar to a pyramid that is short and fat at the bottom. At higher temperatures, the pyramid grows taller and skinnier. This trend continues as the temperature rises, up to what's known as the "absolute high" temperature -- where the pyramid transforms into a single column, stretching from the ground infinitely up toward the sky. This is where things begin to get weird.

If you can somehow push the system one step beyond “absolute high,” the pyramid shape suddenly reemerges, but this time it’s flipped -- each layer now contains more bricks than the one underneath it, with infinitely many bricks at the infinitely tall top. Here comes the even weirder part -- when this happens, the "temperature" in the equation describing the shape of this “pyramid” actually becomes negative.

An ever-expanding and infinitely tall upside-down pyramid may sound too ludicrous to even think about. Ditto for a negative temperature that is somehow hotter than infinite. But if we stop thinking of the particles’ energies as boundless kinetic energies, negative temperature is actually a very real parameter that can be used to describe the distribution of other kinds of energies inside a physical system.

"This is not necessarily the temperature in the classical sense -- there is a distinction between the different ways temperature is used to measure the properties of a system," said Stefan Hilbert, a physicist from Ludwig Maximilian University of Munich in Germany not involved in the paper. "For example, you can have a system with this so-called 'population inversion' -- where there are more parts of the system in an excited state than in a lower energy state."

In other words, physical systems that somehow limit the "pyramid" to a finite number of levels can actually be inverted. To see this mechanism at work, look no further than the unassuming laser pointer.

### Real world applications for an out-of-this-world concept

Every time you click on a laser pointer, you tap into the magic of "population inversion." Atoms are "pumped" from a lower energy level to a higher energy level, and then they fall back down, emitting light in the process.

Today, scientists are findings ways to manipulate other excitable physical systems. Spin -- the entity that determines the magnetic properties of an atom -- is among the hottest topics in negative temperature research.

"Before lasers, people thought if you have a bunch of spins you cannot excite more than half of them because that is [the] hottest possible state," said Kae Nemoto, a researcher from the National Institute of Informatics in Tokyo and an author of the paper.

But scientists have since shown that’s not true. In their paper, Nemoto and her colleagues describe a specific way to set up a spin system such that a part of its population actually prefers to be as inverted as possible. In other words, unlike lasers, where one needs to constantly "pump" atoms into the higher level, parts of their spin system actually flow upward naturally.

"[In lasers], there's a population inversion, but it's not really a steady state. You can populate the excited state, but the atoms are not gonna stay there for a long, long time," said William Munro, a researcher from the Nippon Telegraph and Telephone Corporation and another author on the paper.

Nemoto, Munro, and their colleague Yusuke Hama from the RIKEN Center for Emergent Matter Science in Saitama, Japan, discovered that if there are two separate pockets of atoms with spins sharing a reservoir with a fixed temperature, the two pockets don't necessarily reach an equilibrium in the end.

When the two pockets are equal in size, even when one started with all the spins in the higher state, and the other one all in the lower state, over time, both pockets end up in the middle, with half of the spins in the higher state, and half in the lower.

But something peculiar happens when the two pockets are different sizes. For example, if Pocket A contains more spins than Pocket B, while all the spins in Pocket A are in the higher state and all the spins in Pocket B are in the lower state, then the two do not both relax towards the lowest possible state like that of a laser. Instead, all the spins in Pocket B would flow towards the higher state. In other words, Pocket B actually prefers to be in the most inverted state possible. This revelation can guide future efforts to manipulate the magnetic systems that are ubiquitous in modern day applications.

"The idea of negative temperatures is important for interpreting the experimental results of many physical systems, especially for these spin systems, " said Hilbert.

Filed under
Author Bio & Story Archive

#### Yuen Yiu

Yuen Yiu is a former staff writer for Inside Science. He's a Ph.D. physicist and fluent in Cantonese and Mandarin. Follow Yuen on Twitter: @fromyiutoyou.