A team of physicists has computationally constructed a two-dimensional material that behaves like a paradox: it is disordered like a liquid at the atomic level yet mechanically rigid like a crystal. The simulated “ideal glass,” built from jammed disk packings with zero configurational entropy, represents a state that scientists have theorized about for nearly eight decades but never directly produced. The work, attributed to Bolton-Lum, Dennis, Morse, and Corwin, was published in Physical Review Letters in early 2026 and highlighted as an Editors’ Suggestion, according to indexing records.
Kauzmann’s 78-Year-Old Puzzle
The story begins in 1948, when chemist Walter Kauzmann noticed something troubling about supercooled liquids. As a liquid cools below its melting point without crystallizing, its entropy drops. Kauzmann realized there must exist a temperature at which the entropy of the supercooled liquid would cross that of the crystal, a scenario that seemed physically impossible because a disordered state should not be more ordered than a crystalline one. This hypothetical crisis point, now known as the Kauzmann temperature, implied that if cooling could continue without crystallization, the liquid’s configurational entropy would vanish.
That crossing point suggested a dramatic outcome. A supercooled liquid whose entropy falls below that of the crystalline phase must undergo massive freezing, becoming a glass with essentially no remaining configurational freedom. The hypothetical endpoint of this process, a glass with zero excess entropy over the crystal, became known as the “ideal glass.” For decades, researchers debated whether this state was a genuine thermodynamic destination or merely a mathematical extrapolation of data taken far from equilibrium. The tension between thermodynamic and dynamic interpretations of the glass transition has driven extensive study of fragility and excess heat capacity in supercooled systems, as scientists tried to infer what happens at temperatures that experiments cannot directly reach.
Building the Impossible in a Computer
The new study sidesteps the practical barriers that have blocked experimental access to the ideal glass. In a real laboratory, cooling a liquid slowly enough to reach zero configurational entropy would take longer than any feasible experiment. Molecules get trapped in local energy minima long before they can find the deepest possible arrangement. The computational approach instead constructs ideal jammed packings of two-dimensional disks directly, using optimization algorithms to search for mechanically stable configurations that maximize density while eliminating alternative arrangements.
The resulting structure has zero configurational entropy, meaning that, at the chosen density, there is effectively only one distinct way the particles can be arranged, up to trivial symmetries, just as in a perfect crystal. But unlike a crystal, the arrangement has no repeating lattice. The particles sit in a disordered pattern that nonetheless achieves anomalously high packing fraction and exhibits large bulk and shear moduli, giving it mechanical stiffness comparable to a crystalline solid. The material is also hyperuniform, a property in which density fluctuations are strongly suppressed over large length scales in a way that ordinary glasses do not achieve.
Hyperuniformity: The Hidden Order in Disorder
Hyperuniformity is the structural feature that bridges the gap between liquid-like disorder and crystal-like rigidity in the ideal glass. In a typical liquid or conventional glass, if you sample the density in different regions, you find significant random variation that scales with the size of the sampling window. In a hyperuniform material, those fluctuations shrink more rapidly as the window grows, approaching the near-perfect uniformity of a crystal without adopting a crystal’s periodic structure.
This property has practical consequences for stability. Research on hyperuniform disordered solids has shown that they can exhibit crystal-like stability, with heating protocols and fictive temperature measurements confirming that hyperuniform glasses resist thermal degradation far better than conventional glasses formed at similar cooling rates. Separately, earlier theoretical work established a “perfect glass” concept, describing a hyperuniform and disordered structure that is mechanically stable down to absolute zero and characterized by large elastic moduli and an absence of crystalline or quasicrystalline order. The new two-dimensional ideal glass fits squarely within this framework, providing a concrete computational realization of what had largely been a theoretical construct.
Why Crystal-Hard and Liquid-Like Is Not a Contradiction
The phrase “crystal-hard but liquid-like” captures a genuine duality rather than a contradiction. Crystals derive their stiffness from long-range periodic order: every atom has a well-defined set of neighbors, and the structure resists deformation because displacing one atom forces a coordinated shift of many others in a predictable way. The ideal glass achieves comparable stiffness through a different mechanism. Its particles are packed so tightly and uniformly that the structure resists compression and shear even without periodicity. The high bulk and shear moduli reported in the simulations confirm this crystal-like mechanical response in a material that, structurally, looks nothing like a crystal.
A follow-up preprint proposes an explanation for why this works. According to that study, local centrosymmetry in the particle arrangements accounts for the high stability and atypical vibrational and mechanical signatures of ideal and ultrastable two-dimensional glasses. In other words, while the overall pattern is disordered, each particle’s immediate neighborhood has a balanced, symmetric quality that locks the structure in place. This local order without global order is what separates the ideal glass from ordinary glasses, which lack such pervasive local symmetry, and from crystals, which extend symmetry to every scale.
What Configurational Entropy Actually Measures
Configurational entropy is a thermodynamic measure of how many distinct arrangements of particles are accessible at a given energy or density. In a high-temperature liquid, atoms or molecules constantly rearrange, exploring a vast number of configurations; the configurational entropy is large. As the liquid is cooled and approaches the glass transition, motion slows and the system becomes confined to a smaller region of its energy landscape. The number of distinct amorphous arrangements that the system can still explore shrinks, and so does the configurational entropy.
In practice, configurational entropy in supercooled liquids is inferred indirectly from calorimetric measurements and extrapolations. Analyses of thermodynamic data on glass formers compare the entropy of the supercooled liquid with that of the corresponding crystal, integrating differences in heat capacity to estimate how much configurational freedom remains. These studies generally support the idea that, if crystallization could be avoided indefinitely, the extrapolated configurational entropy would vanish at a finite temperature close to Kauzmann’s original estimate.
The computational ideal glass effectively jumps to the endpoint of that extrapolation. By constructing a jammed configuration with zero configurational entropy at a fixed density, the researchers demonstrate that such a state is not just a mathematical curiosity but a well-defined mechanical object. In doing so, they give concrete meaning to Kauzmann’s “entropy crisis”: instead of an unphysical situation where a liquid becomes more ordered than a crystal, the system transitions into a distinct amorphous solid whose disorder is purely structural, not configurational.
Implications and Open Questions
The existence of a mechanically stable, hyperuniform ideal glass has several implications. First, it supports thermodynamic pictures of the glass transition in which a genuine underlying state with vanishing configurational entropy exists, even if experiments cannot reach it directly. Second, it suggests design principles for ultrastable amorphous materials: promoting hyperuniformity and local centrosymmetry could yield glasses with exceptional rigidity and thermal stability, potentially useful for photonics, protective coatings, or precision resonators.
At the same time, the work raises new questions. The current construction is strictly two-dimensional and relies on idealized disk interactions; whether similarly unique, hyperuniform packings exist in three dimensions for realistic atomic or molecular potentials remains an open problem. It is also unclear how closely experimental vapor-deposited ultrastable glasses approach the ideal limit, or whether kinetic protocols can be tuned to systematically increase hyperuniformity and local symmetry. Finally, the relationship between the vibrational spectra of these ideal glasses and the anomalous low-temperature excitations seen in ordinary glasses is only beginning to be explored.
By turning a long-standing thermodynamic paradox into a tangible, if virtual, material, the new simulations give researchers a concrete target for theory and experiment alike. The ideal glass is no longer just a line on an extrapolated plot. It is a specific, rigid, disordered structure that can be analyzed, perturbed, and, perhaps one day, approximated in the laboratory.
More from Morning Overview
*This article was researched with the help of AI, with human editors creating the final content.
