If ultra-stable glass’s exceptionally low heat capacity really does come from having fewer two-level systems, then ideal glass naturally corresponds to the state with no two-level systems at all. “It’s just perfectly, somehow, positioned where all the atoms are disordered–it doesn’t have a crystal structure–but there’s nothing moving at all,” said David Reichman, a theorist at Columbia University.

Furthermore, the drive toward this state of perfect long-range amorphous order, where each molecule affects the positions of all others, could be what causes liquids to harden into the glass we see (and see through) all around us.

In this emerging picture, when a liquid becomes a glass, it’s actually attempting to transition to the ideal-glass phase, drawn by a fundamental pull toward long-range order. The ideal glass is the endpoint, Royall said, but as the molecules try to crowd closer together, they get stuck; the increasing viscosity prevents the system from ever reaching the desired state.

Recently, groundbreaking computer simulations were used to test these ideas. Simulating ultra-stable glass on a computer used to be infeasible because of the extraordinary computing time required for the simulated molecules to crowd together. Two years ago, though, Berthier found a trick that allowed him to speed up the process by a factor of 1 trillion. His algorithm picks two particles at random and swaps their positions. These shake-ups help the simulated liquid stay unstuck, allowing molecules to settle into snugger fits–just as the ability to swap two ill-fitting shapes would help in Tetris.

In a paper that’s under review for publication in Physical Review Letters, Berthier, Scalliet, Reichman and two co-authors reported that the more stable the simulated glass, the fewer two-level systems it has. As with Hellman’s and Ramos’ heat capacity measurements, the computer simulations suggest that two-level systems–competing configurations of groups of molecules–are the source of glass’s entropy. The fewer of these alternative states there are, the more stability and long-range order an amorphous solid has, and the closer it is to ideal.

The theorists Vassiliy Lubchenko of the University of Houston and Peter Wolynes of Rice University suggested back in 2007 that ideal glass should have no two-level systems. “I’m quite happy with Berthier’s result,” Wolynes said by email.

The Amber Anomaly

But then there’s that amber.

Ramos and his collaborators published their comparisons of old and “rejuvenated” samples of the yellow glass in Physical Review Letters in 2014. They found that the 110-million-year-old amber had grown about 2 percent denser, in line with ultra-stable glass. This should suggest that the amber had indeed stabilized over time, as little groups of molecules slipped, one by one, into lower-energy arrangements.

But when the Madrid team cooled the ancient glass nearly to absolute zero and measured its heat capacity, the results told a different story. The aged amber had the same high heat capacity as new amber–and all other ordinary glass. Its molecules seemed to be tunneling between just as many two-level systems as usual.

Why didn’t the number of two-level systems drop over time as the amber stabilized and became denser? The findings don’t fit.

“I really like the experiments on amber, but making an amber glass is sort of a messy process,” said Ediger, the originator of the vapor-deposition method. “It’s basically tree sap that over time chemically changes and solidifies as well as ages.” He thinks impurities in the Spanish amber might have sullied the heat capacity measurements.

Researchers plan to do further experiments on amber, as well as lab-made and simulated glass, hoping to uncover more details of two-level systems and to get closer to the putative ideal state. Reichman noted that it may never be possible to prove its existence with complete certainty. “Maybe one day we will know, at least on the computer, how to precisely pack particles in a way that would be the ideal glass we are looking for,” he said. “But we would then have to wait a very long time–too long–to see if it remains stable.”

Editor’s Note: Ludovic Berthier and David Reichman have received funding from the Simons Foundation, which also supports Quanta, an editorially independent publication. Simons Foundation funding plays no role in their coverage.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

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