Fifth State of Matter May Defy the Second Law of Thermodynamics

Why does food stay solid in your freezer? Why does your tea cool down if you leave it out? Why is your dining room table a uniform temperature, instead of concentrating all its heat in a tiny corner?

While these questions may seem trivial—after all, that’s the way the world is—it took decades of work for some of the most brilliant minds in physics to work out the answers. Superstars like J. Willard Gibbs, Ludwig Boltzmann, and James Clerk Maxwell worked tirelessly at the end of the 19th century to formulate what’s today known as statistical mechanics and thermodynamics, descriptions of how energy is distributed throughout a system.

Although you could spend a Ph.D. thesis delving into the nuances of this theory, thermal physics is at its heart an extremely elegant solution to a complex problem: essentially, it predicts that as time goes on, objects that are in contact with each other will tend to reach equilibrium. Rather than allowing different parts of a system to hoard energy, or permitting warmer objects to “steal” heat from their cooler neighbors, thermal physics requires that in the long term any system tend towards a uniform temperature. This means that your ice cream will reach the same temperature as your freezer, your tea will adjust to the temperature of your house, and your table will resist the urge to suddenly burst into flames.

Or so we thought.

Incredibly, a group at the Institute for Basic Science (IBS) in South Korea has just published some findings in Physical Review Letters indicating that the traditionally robust laws of thermodynamics may not hold up in the quantum world. Instead, they argue that for certain situations equilibrium is not reached, regardless of the amount of time allowed to pass. As they explain, this is like a slice of pizza that starts out unevenly heated—but instead of equalizing over time, the hot and cold spots just stay there indefinitely!

The team, composed of theoretical physicists Thudiyangal Mithun, Yagmur Kati, Carlo Danieli, and Sergej Flach, started off examining what is known as a Gross-Pitaevskii lattice. Although the terminology is daunting, this is just a mathematical model that characterizes energy and particle distributions for a variety of situations—so many, in fact, that Danieli and Flach refer to it as “one of the canonical models of mathematical physics”. Among others, these scenarios include Bose-Einstein condensates (which will be described in more detail below) and certain types of interactions between light and matter.

With the assistance of powerful computers, the group investigated the long-term behavior of this model’s energy distribution and were surprised to find that under certain conditions, hot and cold spots just don’t go away. Instead, they remain “frozen” in place, in direct violation of classical thermal physics! This phenomenon has been dubbed a “dynamical glass phase”, a term reminiscent of its simultaneous stability and fragility.

What’s really going on here? The short answer is that it’s just too early to tell. All of this work was theoretical, so one of the next steps should be to test it in the laboratory by cooling ultracold atomic gases to temperatures near absolute zero. This creates what’s known as a quantum Bose-Einstein condensate (BEC), a special state of matter where quantum phenomena become readily apparent. As previously mentioned, BECs are also described by the Gross-Pitaevskii lattice, so they should display dynamical glass properties when prepared a certain way.

This image shows the change in atoms’ behavior as they cool from a gaseous state, left, to a BEC, at right. While the height of the chart represents the number of atoms, the position of the “bump” doesn’t actually correspond to position: these are velocity distributions. As the atoms transition to a BEC, they all begin to move with close to the same velocity, rather than the bell-curve distribution typical of thermodynamics at higher temperatures.
Image Credit: NIST/JILA/CU-Boulder. Public Domain

The IBS team—being a part of the IBS Center for Theoretical Physics of Complex Systems—plans to continue and deepen its theoretical and computational studies and to extend them to other system classes. One of the hottest tasks is to find a way to clearly classify models that have a dynamical glass state.

As it turns out, this work isn’t the first to contradict statistical mechanics. In the mid-20th century, another group of theoretical physicists and mathematicians discovered limitations on the theory, which led to the subsequent development of what has come to be known as Kolmogorov-Arnold-Moser theory (or KAM theory) in their honor. However, KAM theory, too, breaks down when applied to large numbers of particles, what is known in the field as many-body systems. In contrast, the phenomenon the IBS team has uncovered should apply regardless of the system’s size.

Although these results could prove a crucial breakthrough in our understanding many-body interactions in the quantum world, it’s unlikely to change the way we interpret freezers, tea, or tables. After all, the Gross-Pitaevskii lattice on which all this work hinges represents systems that are very much out of the ordinary. Instead, this research is a great example of what happens when you push a physics theory to its breaking point.

So maybe don’t toss your thermo textbook just yet.

—Eleanor Hook

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