Glass Transition Theory

Speculative If the slowdown that turns a liquid into a glass has a thermodynamic cause — a length over which amorphous order is fixed, growing as the liquid cools — then the glass transition temperature of a material becomes something a theory computes rather than something a laboratory measures one compound at a time. The condition comes first, because it is not established. No measurement in a molecular liquid has produced that length across the range where the slowdown actually happens, and section 7 says exactly what would.

Established The magnitude is best stated as the size of the extrapolation industry currently performs without a theory to guide it. Between the two reference viscosities that bracket a glass-former — 10⁻⁵ Pa s in the hot melt and 10¹² Pa s at the conventional glass transition — lie seventeen orders of magnitude, and in a fragile liquid most of them arrive over a very small temperature change: ortho-terphenyl’s relaxation time rises by a factor of 10¹⁰ for a temperature drop of ten per cent. Annealing schedules, amorphous-drug shelf lives, fibre draw temperatures and phase-change memory retention are all set by fitting that curve in the decade where it can be measured and extrapolating it into the decades where it cannot. Every one of those extrapolations is an empirical tax, and nobody has published a figure for what the tax costs.

Frontier The one place the prize has already been collected is vapour deposition, and it was found by accident rather than by theory. Depositing an organic glass-former onto a 5 nm rubbery substrate produces, in 2.5 hours, a film up to 2.5 per cent denser than the liquid-quenched glass — a state the same apparatus would otherwise reach only at a deposition rate ten million times slower, which the authors put at about 3,000 years. That is a measured seven-order-of-magnitude shortcut, in one material, by one route, and the reason it matters here is that nobody can yet say which other materials or which deposition windows will do the same thing. A theory of the glass transition is, concretely, the thing that would turn that scan into a calculation.

Handwave The gains accrue to deposition-based industries and to formulators, not to a consumer, and the condition on all of it is the length in the first paragraph. Organic light-emitting-diode stacks, chalcogenide memory films, metallic-glass coatings and amorphous pharmaceutical dispersions are the buyers; there is no product at the end of this page that a household would recognise. And the upside is real only if the deposition window can be predicted instead of scanned, which is the same requirement as predicting the transition itself. Section 5 is about why that requirement has resisted thirty years of work by two camps who cannot agree on what would settle it.

Established A glass is a liquid that has stopped flowing on the timescale of the observation, and the glass transition is the temperature at which that happens. The working definition is operational rather than thermodynamic: the transition temperature T_g is fixed at a viscosity of 10¹² Pa s, equivalently 10¹³ poise, a value close to the annealing point of ordinary industrial glass. Nothing diverges there, no latent heat is released, and no symmetry is broken. What happens is that a liquid’s structural relaxation time crosses the time the experimenter is prepared to wait, and the material falls out of equilibrium.

Established The number that makes this a physics problem rather than an engineering convention is how fast the viscosity climbs. Across the cooling range of a glass-former the viscosity can rise by as much as seventeen orders of magnitude within a temperature interval of a few hundred kelvin, and the rise is not Arrhenius. Liquids are sorted by how sharply they depart from Arrhenius behaviour — the steepness index, or fragility — and measured values run from 43 for arsenic triselenide through 62 for selenium to 103 for ortho-terphenyl. Strong liquids climb almost exponentially in inverse temperature; fragile ones hold out and then fall off a cliff.

Frontier The theoretical problem is that this enormous kinetic effect is accompanied by almost no structural change. A diffraction pattern taken on a fragile liquid at 1.2 T_g and at T_g looks nearly identical, while the relaxation time between those two points has grown by ten decades or more. Something in the liquid is changing by a factor of 10¹⁰ and the two-body structure is not reporting it. Every theory of the glass transition is an answer to that one observation.

Frontier There are two live answers and they are not compatible. The random first-order transition theory — RFOT — says the liquid is developing genuine amorphous order: below a crossover temperature it breaks into a mosaic of regions, each frozen into one of an exponentially large number of locally stable packings, and the mosaic length grows as the number of available packings shrinks. Relaxation then costs a collective rearrangement whose free-energy barrier scales with that length, and the slowdown is thermodynamic in origin. Dynamic facilitation says the opposite: nothing thermodynamic is happening, the liquid contains a dilute gas of localised excitations whose concentration falls with a simple Boltzmann law, relaxation propagates because an excitation creates its neighbours, and the whole phenomenology follows from kinetics with no growing static length required.

Speculative A third family, older than both and quietly influential, says the barrier is elastic. Shoving and elastic models make the activation energy proportional to the instantaneous shear modulus, so the slowdown is a stiffening rather than an ordering. A 2026 assessment reports that global elasticity accounts for only about half the observed variation in activation energy while a purely local elasticity overshoots it by about a factor of two, which is a specific quantitative failure rather than a vague one and is why the same authors propose an excitation spectrum instead.

Handwave Mode-coupling theory sits underneath all of this as a well-defined approximation that is wrong in a known direction. It predicts a genuine dynamical arrest at a temperature T_mct; in real liquids and in simulations that temperature is a crossover rather than an arrest, because relaxation continues below it by activated processes the theory does not contain. The field uses T_mct as a landmark and does not defend it as a transition.

Established The oldest piece of evidence in the dispute is an entropy extrapolation made in 1948 and it has never been either confirmed or disposed of. Kauzmann pointed out that the excess entropy of a supercooled liquid over its crystal, extrapolated below T_g, hits zero at a finite temperature now called T_K, which would be absurd. RFOT takes this seriously and identifies T_K as a real ideal-glass transition hidden below the experimental window. Facilitation treats it as an artefact of extrapolating a curve past the point where the material still equilibrates. Both readings survive because nobody can equilibrate a laboratory liquid below T_g to check.

Established This section is the measured record, and it opens with the anchor the commission named, corrected. The commission described the phenomenon as viscosity rising fourteen decades over a narrow window. The direction is right and the arithmetic needs a stated baseline: fourteen decades is the span from a melt viscosity of about 10⁻² Pa s to the conventional T_g at 10¹² Pa s, while the reference viscosities used in the viscometry literature, 10⁻⁵ and 10¹² Pa s, bracket seventeen. The load-bearing half of the claim is the window, not the count, and the window has a number: for ortho-terphenyl the relaxation time increases by a factor of 10¹⁰ as the temperature drops by ten per cent.

Established The second half of the anchor — vapour-deposited ultrastable glasses reaching millennia-equivalent stability in hours — is verified, and the equivalence it asserts is narrower than it sounds. Depositing the organic semiconductor TPD onto a 5 nm poly(dimethylsiloxane) layer gives glasses up to 2.5 per cent denser than the liquid-quenched material within 2.5 hours of deposition, matching what the same process would produce at a rate ten million times slower, which the authors convert to about 3,000 years. Surface-mediated equilibration in that work extends up to 170 nm from the interface, which is itself a surprise: the mobile surface layer was supposed to be a few nanometres.

Frontier The same effect is reproducible in metals, at substrate temperatures far below where the mechanism was thought to work. Ion-beam-assisted deposition of Zr₄₆Cu₄₆Al₈ at a substrate temperature of only 0.43 T_g and a rate of 1.01 nm per minute produced glasses whose T_g is 757 K, 59 K above the ordinary glass, with a free-surface residence time estimated at about 17 s. The authors state that liquid-cooled glasses would need thousands of years of ageing or more to reach comparable properties.

Established And here the commission’s phrase “millennia-equivalent” breaks, in a way that matters for the whole subject. Amber from a Spanish deposit, hyperaged for 110 million years, was measured against annealed and rejuvenated samples of itself: below one kelvin the specific heats of all the samples were identical within experimental error. The two-level systems and the boson peak — the low-temperature excitations that vapour-deposited ultrastable glasses are reported to suppress — survived a hundred million years of ageing untouched. Ageing and vapour deposition do not reach the same state. Deposition is not a fast-forward button on time; it is a different route to a different place, and any statement that equates the two is describing fictive temperature and density only.

Established The viscosity of an ultrastable glass has been measured directly, at values that are hard to state without stopping to check them. Vapour-deposited indomethacin films with fictive temperatures from 281 K to 301 K — a maximum gap of 34 K below T_g for the most stable case, deposited at a substrate temperature of 266 K — were probed by relating ultraviscous flow to the elastic properties of the glass, giving viscosities up to exapoise values, against 10¹¹ to 10¹³ poise at the ordinary glass transition. The authors observe that these states populate free-energy regions as low as semi-fossilised resins aged for thousands of years.

Frontier On the theory side, the single sharpest result of the last decade is a simulation trick, and it is a trick that appears to falsify a theory. The swap Monte Carlo algorithm exchanges the diameters of particles that may be far apart. It leaves the Hamiltonian, and therefore every static quantity including any amorphous-order length, exactly unchanged. Under ordinary local dynamics the relaxation time at the computational glass transition satisfies τ_α/τ₀ of order 10¹⁵; with swap moves allowed it is only about 10² to 10³. Twelve to thirteen orders of magnitude are bought purely by changing the kinetic rule.

Frontier Wyart and Cates drew the obvious inference and added a second, independent bound. Their argument is that the underlying free-energy landscape is unaffected by the move set, so any static length must be identical with both dynamics and any collective barrier derived from it must be identical too; since the relaxation times differ by thirteen decades, local barriers rather than collective ones must control relaxation. Separately they argue from the observed Stokes–Einstein decoupling, about a factor of 10³, that the growth of a static length cannot account for more than roughly three decades of the increase in τ_α. Against fourteen or seventeen decades, three is a minority shareholding.

Frontier The RFOT camp’s reply is not a denial of the numbers but a reinterpretation of what swap does. Berthier, Biroli, Bouchaud and Tarjus argue that a local mechanism cannot explain the phenomenology, and explain swap’s efficiency as a postponed onset of glassy dynamics — the algorithm explores configuration space efficiently in the regime where the physical dynamics is already dominated by activated crossings, a situation they call crumbling metastability, and they point to nucleation as a known case where changing the local dynamical rule circumvents a barrier of genuinely thermodynamic origin. Whether this is a real mechanism or a rescue is the central unresolved question of section 4.

Frontier The Kauzmann extrapolation has now been done as a direct equilibrium computation, and the answer was zero. A two-dimensional atomistic glass was equilibrated all the way to zero temperature at system sizes of 44, 55, 66 and 77 particles, with partial equilibration at 176 and 704. The Kauzmann temperature measured at N = 55 is 0.057 and falls systematically with system size, extrapolating to T_K → 0 in the thermodynamic limit; the reference landmarks in the same units are T_g ≈ 0.15, T_mct ≈ 0.3 and an onset near 0.5. Three independent methods for the configurational entropy agreed that it vanishes only at zero temperature, and the authors state they find no sign of a finite-temperature entropy crisis.

Speculative That result is not the defeat of RFOT it first appears to be, and the reason is dimensionality. The same work reports a jump in the overlap order parameter at the transition and a hierarchical, nested organisation of low-lying states of the kind mean-field theory predicts, and describes the outcome as a zero-temperature critical point. Two dimensions is the hard case for any theory built on a mosaic, because fluctuations are strongest there; the finding that the ideal glass transition survives but is pushed to zero temperature is compatible with RFOT having a lower critical dimension at or near two. No equivalent equilibrium computation exists in three dimensions, which is why section 6 asks for one.

Established The point-to-set length — the quantity the commission nominated as decisive — has already been measured in an experiment, and it grew. In a two-dimensional colloidal glass-former, pinning an amorphous wall of particles and measuring how far its influence propagates gave the first experimental evidence of growing point-to-set correlations in a glass-forming liquid, with ξ_PTS rising monotonically with area fraction across roughly 0.68 to 0.79. The same measurement found the dynamic correlation length growing faster than ξ_PTS and, more awkwardly, non-monotonically, with the rearranging clusters string-like at low density and compact at high density.

Frontier That experiment did not settle the dispute, and the reason it did not is the reason section 7 has to restate it. A growing static length is necessary for RFOT but not sufficient to establish it; what RFOT needs is for the length to grow enough, with the right exponent, to generate the observed barrier. The theory’s own scaling makes the mosaic size ℓ = [Υ/(TΣ)]^1/(d−θ) with θ ≈ 1.5 in three dimensions and about 1 in two, and log τ scaling as ℓ^ψ with an exponent its own proponents describe as surprisingly small, ψ ≲ 1, with fits giving a composite exponent of about 0.5 ± 0.2 across a broad range of materials. A length that doubles has to do fourteen decades of work, and the exponents that let it are the ones that are fitted.

Established The facilitation camp has its own experiment in the same colloidal system, by overlapping authors, and it also came out positive. Approaching the glass transition by random pinning rather than by cooling, the concentration of excitations fell by more than a factor of three as the pinned fraction rose from 0.03 to 0.12 at an area fraction of 0.71, while the structural relaxation time rose by a factor of four and the facilitation volume grew. Both a static length and a facilitation structure grow on approach to the same transition, in the same material, measured by the same group.

Established The most careful single experiment in deep supercooling was done on colloids that were left alone for a hundred days. Poly(methyl methacrylate) particles of 270 nm radius and about 8 per cent polydispersity, Brownian time 34 ms, imaged by three-dimensional stimulated-emission-depletion microscopy, reached relaxation times about a thousand times the mode-coupling crossover. The excitation concentration followed a Boltzmann law with energies 10.5 ± 0.6 and 16.3 ± 0.4 for two compositions; the cooperatively rearranging regions formed on a timescale tracking τ_α^0.8; the fraction of excitations found inside such regions rose from below 10 per cent to 60 per cent at the lowest temperatures; and a modified Adam–Gibbs relation held with exponent 0.6 ± 0.1 while the configurational entropy extrapolated to a Kauzmann temperature close to the Vogel–Fulcher temperature.

Frontier The authors of that experiment declined to declare a winner, and their reason is the most useful sentence in the recent literature. They report that both dynamic and thermodynamic theories are compatible with their data, and suggest that the separation of timescales between excitations and cooperatively rearranging regions leaves room for excitations to accumulate into the cooperative objects the other theory describes. That is not a fudge. It is the observation that the two theories may be describing the same events at different resolutions, which is a third position and is currently unfalsified.

Frontier In molecular liquids, the only measurement that reaches amorphous order at all is a nonlinear dielectric response, and it favours the thermodynamic reading. Applying fields up to 78 MV/m to glycerol and propylene carbonate and detecting the fifth harmonic, the transient correlated domains were found to be compact, with fractal dimension 3, and the fifth-order susceptibility scaled as the square of the third-order one as the amorphous-order picture predicts. The authors state that this provides strong support for theories based on thermodynamic amorphous order rather than on kinetically constrained models.

Frontier The counter-programme is to measure the excitations directly, and in 2025 it produced a parameter-free prediction. A systematic extraction of localised excitations from simulated glass-formers gave a density of states N(E) ∝ (E − E_g)^a with a ≈ 2.7, and the shift of the gap E_g with temperature reproduced the observed change in activation energy with no fitting. The excitation geometry separated into a temperature-independent core — maximum displacement scaling as E^1/3, volume as E^−1/3 — and a temperature-dependent far field. Used as a predictor of which particles move, it reached a Spearman correlation of about 0.7 with the measured propensity.

Frontier Machine learning predicts glassy dynamics well and explains it not at all, and the field has said so in print. A 2025 multi-author roadmap reports graph neural networks reaching Pearson correlations of about 0.85 with particle propensity at τ_α, against below 0.6 for physics-motivated descriptors such as density, hexatic order and potential energy, and states plainly that machine learning does not settle the theoretical dispute. A 2026 review of colloidal vitrification reaches a compatible conclusion from the other side: order-agnostic measures — excess entropy, point-to-set lengths, machine-learned softness, intermediate-range order and soft modes — do link structure to dynamics, provided the correlations considered extend well beyond the first neighbour shell.

Established One widely cited phenomenon was withdrawn in 2025 by better measurement, which is the cleanest event in this brief. The fragile-to-strong crossover reported in germanium–selenium chalcogenides was re-examined across four compositions at 5, 10, 15 and 20 atomic per cent germanium, using three viscometry techniques over about thirteen orders of magnitude. The data are described by a single steepness index with no crossover, and the earlier observations are attributed to the oscillating-cup method, which the authors show disagrees with capillary and parallel-plate measurements by nearly one order of magnitude. A fourteen- or seventeen-decade quantity measured to one order of magnitude is a reminder that in this field the instrument is part of the theory.

Speculative Simulation has also begun to test the two pictures against each other by watching a glass equilibrate rather than by measuring a length. Heating and cooling a swap-equilibrated two-dimensional glass across its transition produced a marked asymmetry: domains of the new state appear and grow during heating, at a front speed of about 1.57 × 10⁻³ particle diameters per time unit, with no waiting time of the kind nucleation requires, and they are absent during cooling. The point-to-set length in the same system is of order one particle diameter. The authors read the asymmetry, and the super-diffusive roughening of the interface, as evidence that facilitation rather than nucleation governs equilibration, and reproduce the same signatures in plaquette models that contain no thermodynamic transition at all.

Handwave The honest summary of the measured record is that both camps can point to a positive result and neither can point to a decisive one. A static length grows; facilitation grows; nonlinear dielectrics favour amorphous order; swap dynamics favours local barriers; the Kauzmann transition in two dimensions sits at zero temperature but retains the structure RFOT predicts. The dispute is thirty years old and has not been resolved by adding data, which is a hint about what kind of experiment is missing rather than about which theory is right.

Frontier Question one: does a growing static length control the slowdown, or merely accompany it? This is the dispute in its sharpest form. Both sides agree a length grows in simulation and now in colloid experiment; they disagree about whether it does the work. The quantitative test is whether log τ scales as the length raised to an exponent ψ ≲ 1 over a range where the length is independently measured, and no experiment has yet produced both quantities in the same molecular sample over more than a decade or two of relaxation time.

Frontier Question two: is the swap result a falsification or a clue? If changing the move set can buy thirteen decades while leaving every static quantity fixed, then either the static quantities are not what sets the barrier, or the physical dynamics contains a bottleneck that swap removes and that the static quantities do not capture. The second reading is the crumbling-metastability argument. It is coherent, it is defended by the theory’s originators, and it has the uncomfortable property of being hard to distinguish from an accommodation.

Speculative Question three: is facilitation fundamental or emergent? Kinetically constrained models assume facilitation and reproduce much of the phenomenology, which proves sufficiency rather than necessity. The live question is whether, in an atomistic liquid, facilitation is a derived consequence of the excitation spectrum and local elasticity or a primitive of the dynamics. The 2025 excitation work, with its exponent of 2.7 and its parameter-free activation-energy prediction, is the strongest argument yet for derived; it is one line of work by one group of collaborators and has not been reproduced independently.

Speculative Question four: what is the lower critical dimension of the ideal glass transition? The two-dimensional equilibrium computation putting T_K at zero is consistent with a lower critical dimension of two, in which case three-dimensional glasses would have a genuine finite-temperature ideal glass transition and two-dimensional ones would not. It is equally consistent with there being no ideal glass transition in any finite dimension and the two-dimensional result being the general case. Nobody has done the three-dimensional computation.

Speculative Question five: why does vapour deposition work, and how far does the surface reach? The standard account is enhanced surface mobility: molecules arriving at a free surface explore many configurations before being buried. The 2024 soft-substrate result, in which surface-mediated equilibration extends up to 170 nm and the substrate modulus controls the density at fixed deposition conditions, is not obviously contained in that account. Either the mobile layer is far thicker than assumed, or the substrate is doing something mechanical that the surface-mobility picture does not describe.

Speculative Question six: are two-level systems and the boson peak a separate problem or the same one? Vapour-deposited ultrastable glasses are reported to suppress the tunnelling two-level systems that dominate glass thermodynamics below one kelvin, while 110 million years of natural ageing suppressed nothing. If the low-temperature excitations are controlled by the same landscape structure as the transition itself, that dissociation is a strong constraint on any theory. If they are a separate sector, it is a coincidence. No theory currently predicts which.

Handwave Question seven: is the field asking a well-posed question at all? A serious minority position is that the glass transition is not a single phenomenon with a single cause, that strong network liquids and fragile molecular liquids arrest for different reasons, and that the search for one theory covering silica, ortho-terphenyl, a metallic alloy and a colloidal suspension is a category error. The 2026 local-excitation review edges towards this when it concludes that an alternative description is needed at least for some materials.

Established The first bottleneck is time, and it is not negotiable. The conventional glass transition is defined by a relaxation time of order 100 s. Molecular dynamics integrates femtosecond steps. The gap is about seventeen orders of magnitude, and it is the same seventeen orders that make the phenomenon interesting, so the computational problem and the physical problem are the same size by construction.

Frontier Swap Monte Carlo closed most of that gap and in doing so created the field’s central methodological dispute. It reaches, in equilibrium, states whose physical relaxation time would be of order 10¹⁵ times the microscopic time — below the experimental glass transition. Every recent thermodynamic result in this brief, including the direct Kauzmann computation and the equilibration-asymmetry study, rests on it. If the RFOT reading of swap is right, the configurations it produces are the correct equilibrium ones and the method is sound; if the Wyart–Cates reading is right, the method is still sound but its very success is evidence against the theory it is being used to test. The tool and the question are entangled.

Established The second bottleneck is that you cannot pin a molecule. Point-to-set measurement requires freezing a subset of particles and watching how far their influence reaches. In simulation and in colloids this is a routine operation. In a molecular liquid there is no handle: the nearest available approach is soft pinning, in which a dilute concentration of larger, slower molecules acts as an imperfect pin, demonstrated with sorbitol and glucose in glycerol and validated against four model glass-formers. It measures a pinning susceptibility whose peak is argued to track the static length, which is a proxy for a proxy.

Frontier The third bottleneck is that the only direct probe of amorphous order in molecular liquids requires enormous electric fields. Extracting the fifth-order dielectric susceptibility means applying fields up to 78 MV/m and detecting the fifth harmonic against a background dominated by the linear response. Very few laboratories in the world do it, the signal falls with the fifth power of a small parameter, and the interpretation depends on a theoretical relation between susceptibility order and domain compactness that the experiment is simultaneously testing.

Established The fourth bottleneck is viscometry itself. Three standard techniques applied to the same chalcogenide compositions disagree by nearly one order of magnitude, and that disagreement was enough to manufacture a fragile-to-strong crossover that better measurement then removed. When the quantity of interest spans fourteen to seventeen decades, one decade of systematic error is a fifteenth of the entire phenomenon, concentrated exactly where the curvature is being fitted.

Frontier The fifth bottleneck is that colloids are not molecules. The colloidal experiments here are the best-resolved measurements in the field — individual trajectories, direct pinning, real point-to-set numbers — and they are performed on 270 nm particles with Brownian times of tens of milliseconds, needing a hundred days of equilibration to reach a thousand times the mode-coupling crossover. A molecular liquid at T_g is roughly twelve further decades away. The systems where the dispute can be watched are not the systems where it matters.

Speculative The sixth bottleneck is dimensional. A disproportionate share of the strongest recent simulation results are two-dimensional, because two dimensions is where swap works best and where full equilibration to zero temperature at small system sizes is achievable. Two dimensions is also where fluctuation effects are strongest and where mean-field-derived theories are least likely to hold. The results are real; their transferability is an assumption.

Handwave The seventh bottleneck is that nobody has written down what would count as a refutation. RFOT has absorbed the swap result by reinterpreting it; facilitation has absorbed the growing point-to-set length by noting that growth alone proves nothing; both have absorbed the colloidal experiments, which found evidence for each. A theory that can absorb every outcome is not being tested, and this is the cheapest bottleneck on the list to remove and the one with no constituency for removing it.

Frontier The first dependency is a three-dimensional equilibrium configurational entropy computed to zero temperature. The two-dimensional result exists and says T_K → 0 in the thermodynamic limit. Until the same calculation is done in three dimensions, the central quantitative claim of RFOT — that there is a finite-temperature ideal glass transition underlying the experimental one — has been tested only in the dimension least favourable to it.

Frontier The second dependency is an amorphous-order length in a molecular liquid, measured over the range where the slowdown happens. Colloids give the length but not the decades; molecular liquids give the decades but not the length. Soft pinning and fifth-order dielectric susceptibility are the two candidate routes and they have never been applied to the same sample.

Speculative The third dependency is an independent reproduction of the excitation spectrum. The exponent a ≈ 2.7 and the parameter-free prediction of the activation-energy shift are the strongest quantitative claims the local-excitation programme has made. They come from one methodology and one group of collaborators. Until another group extracts the same spectrum from a different family of models with a different algorithm, this is a promising result rather than a settled one.

Established The fourth dependency is metrological and unglamorous: certified viscosity reference liquids and a round-robin across techniques. The 2025 chalcogenide result shows what one decade of instrumental disagreement does to a claimed phenomenon. The field has no equivalent of the interlaboratory comparisons that other precision communities run as a matter of routine.

Handwave The fifth dependency is social and is the precondition for the other five mattering. Two camps, both productive, both well funded, both able to reinterpret the other’s decisive results, have coexisted for three decades. Nothing in the physics prevents a joint pre-registration naming what each theory predicts for a specified measurement and what result each would concede to. Nothing in the sociology has produced one.

Frontier Before naming a decisive experiment this brief has to correct the one it was commissioned with, because the commission’s version has already been run. The commission proposed measuring a growing point-to-set correlation length approaching T_g, on the grounds that RFOT predicts one and dynamic facilitation predicts none. Growing point-to-set correlations were measured directly in a colloidal glass-former and reported as the first experimental evidence of them, and the dispute continued unaffected. The framing fails twice: dynamic facilitation does not predict the absence of a static length, it predicts that a static length is not what sets the barrier; and RFOT needs not merely growth but growth of a specific magnitude and exponent. A yes-or-no measurement cannot discriminate between a theory that needs a number and a theory that is indifferent to it.

Speculative The decisive experiment for this brief is the quantitative version: measure a static amorphous-order length and the relaxation time in the same molecular glass-former across the last four decades of relaxation time approaching T_g, by two independent methods, and test whether log τ scales as that length raised to a power of order unity. The two methods are soft pinning, demonstrated in glycerol with sorbitol and glucose pins, and fifth-order dielectric susceptibility at fields approaching 78 MV/m, demonstrated in glycerol and propylene carbonate. Glycerol is common to both, which is why it is the sample. RFOT survives if the length grows enough to carry four decades of barrier with ψ ≲ 1 and θ ≈ 1.5; it is in serious trouble if the length saturates or requires exponents outside that range; and the local-excitation picture is in serious trouble if the two independent length measurements agree with each other and with the barrier.

Speculative This experiment needs no new hardware, and nobody has assembled it as a single programme. Both techniques exist in working laboratories, the sample is one of the most studied liquids in the field, and the measurement is a campaign rather than an instrument. Its absence is a coordination failure, not a capability gap, which is the most common way a decisive experiment fails to happen.

Frontier Second in rank: the three-dimensional equilibrium Kauzmann computation. Repeat the two-dimensional protocol — full equilibration to zero temperature at system sizes from tens to hundreds of particles, three independent estimators of the configurational entropy, finite-size scaling of T_K — in three dimensions. If T_K extrapolates to a finite value in three dimensions and to zero in two, RFOT gains its first clean dimensional signature and the lower critical dimension is pinned. If it goes to zero in both, the ideal glass transition is a mean-field artefact and one of the two camps has lost its foundation.

Speculative Third: the reheating test proposed in 2026, which extracts the true activation energy by outrunning the temperature dependence of the prefactor. A temperature jump completed within 0.1 to 1 s is effectively instantaneous for the relaxation being probed, so the immediate response reports the barrier at the old structure. Its proposers state this appears achievable with existing apparatus. It discriminates because the local-excitation picture predicts the barrier follows the excitation gap E_g(T) with no fitting, and the thermodynamic picture does not make that prediction.

Speculative Fourth: an experimental analogue of swap. The swap argument’s force comes from holding the Hamiltonian fixed while changing the kinetic rule, which is trivial in a computer and hard in a laboratory. Colloidal mixtures whose particle sizes can be altered in situ would make the comparison real. Nobody has published it; until someone does, the strongest argument against a thermodynamic origin rests entirely on a simulation move that no physical system performs.

Frontier Fifth: the low-temperature dissociation, which is half done and worth finishing. Amber hyperaged for 110 million years shows no suppression of two-level systems or the boson peak, while vapour-deposited ultrastable glasses are reported to suppress the tunnelling systems strongly. Measuring both on the same chemistry — a molecular glass-former available as a natural hyperaged resin, a laboratory-aged sample and a vapour-deposited film — would establish whether the two routes reach different regions of the landscape or merely different depths in the same one.

Speculative Sixth: the devitrification-front measurement in ultrastable films. Ultrastable glasses transform back to the supercooled liquid by fronts that propagate from surfaces, at a speed that is measurable and that carries information about the barrier structure the deposition process built. The simulation counterpart has already produced a front speed of about 1.57 × 10⁻³ particle diameters per time unit and a marked heating-cooling asymmetry that plaquette models with no thermodynamic transition also reproduce. A film-thickness-resolved experimental front speed against fictive temperature would test whether that asymmetry survives in a real material.

Handwave Seventh, and cheapest: a pre-registered adjudication protocol agreed before the next result. Both camps write down, in advance, the measured value of a named quantity that they would accept as refuting their position, and the range they predict. This costs a workshop. Its absence is why a thirty-year-old dispute has survived a growing static length, a growing facilitation volume, a thirteen-decade swap speedup and a zero-temperature Kauzmann transition without anyone conceding anything.

Frontier Eighth, and running already without being called an experiment: interlaboratory viscometry. The 2025 chalcogenide work is in effect a round robin conducted after the fact, and it deleted a phenomenon. Running one deliberately, on certified reference liquids across capillary, parallel-plate and oscillating-cup methods, would establish how much of the published fragility record is instrument rather than material. Given that one decade of disagreement was enough to create a fragile-to-strong crossover, the answer is not obviously small.

Established The engineering requirements of this subject are unusual because most of them are already met, by instruments built for other purposes. Deposition chambers, dielectric spectrometers, confocal and stimulated-emission-depletion microscopes and viscometers all exist; what does not exist is a programme that points several of them at the same sample. The constraint is integration, not capability.

Frontier Ultrastable deposition needs rate and substrate control at a precision that is now a materials-science speciality in its own right. The metallic-glass result used 1.01 nm per minute at a substrate temperature of 0.43 T_g; the organic soft-substrate result used a 5 nm elastomer layer whose modulus, at fixed deposition conditions, set the resulting density. Controlling a substrate’s mechanical compliance as a deposition parameter is not something a standard evaporator does, and the 170 nm reach of surface-mediated equilibration means film thickness is a variable and not a convenience.

Frontier Nonlinear dielectric spectroscopy is the hard instrument. Fields to 78 MV/m across a sample that must not break down, harmonic detection to fifth order, and thermal stability over the hours the measurement takes: this is a small number of laboratories worldwide and the principal reason the molecular-liquid evidence for amorphous order rests on two liquids rather than twenty. Any serious attempt at the decisive experiment of section 7 begins by building or buying access to one of these.

Established The colloidal route needs patience as a capital input. A hundred days of equilibration per state point on 270 nm particles with a 34 ms Brownian time: the apparatus is standard and the schedule is not, which is why the field’s best-resolved data come from a small number of groups.

Frontier Compute is a first-class requirement and a contested one. Swap Monte Carlo is cheap per step and the equilibration it enables is what makes modern glass simulation possible; graph neural networks trained to predict propensity are not cheap and their advantage over simple descriptors — about 0.85 against below 0.6 — is the field’s clearest statement of how much it does not understand. The requirement is not more floating-point operations; it is interpretable models, which is a different research programme. The same tension appears in Autonomous Materials Discovery, where predictive power without mechanism is a recurring difficulty.

Established Metrology is the requirement the field has neglected and the one with the clearest precedent. Certified reference liquids, documented uncertainty budgets per technique and published interlaboratory comparisons are routine elsewhere and absent here, and the 2025 chalcogenide result shows the cost. This is the same argument made in Metrology Infrastructure and in Additive Manufacturing Qualification, where the qualification of an amorphous or partially amorphous material is a schedule item rather than a calculation.

Established Phase-change memory is the adjacent technology where glass physics met a market and lost. Intel’s 3D XPoint used germanium–antimony–tellurium chalcogenide for both the storage element and the ovonic threshold selector, storing bits as the amorphous or crystalline state of a glass-former. Intel discontinued the consumer Optane line in January 2021 and announced the winding down of the division in July 2022; the Lehi fabrication plant was sold to Texas Instruments for 900 million US dollars. Data retention in such a cell is the crystallisation kinetics of a supercooled liquid extrapolated over years, which is exactly the extrapolation this brief is about.

Established Vitrification of high-level radioactive waste is the largest deliberate use of the glassy state, and its design lifetime is an extrapolation of the same curve. Borosilicate glass is the immobilisation matrix of record, and its qualification rests on leach rates and structural stability projected over geological time. Nuclear Waste Solutions owns the repository question; what belongs here is that the projection rests on a theory of ageing that section 3 shows is contested even over laboratory timescales.

Frontier Cryopreservation is the adjacent field where avoiding crystallisation is the entire objective. Vitrification and nanowarming have kept rat kidneys cryopreserved for up to 100 days and restored life-sustaining function after transplantation, using alternating magnetic fields to heat iron-oxide nanoparticles for rapid uniform rewarming. The physics being exploited is the competition between glass formation and nucleation on rewarming, and it is the same competition. Cryonics and Brain Preservation carry the claims and the controversies; this page carries the transition.

Speculative Amorphous pharmaceutical formulation is the largest commercial application of the glass transition and this brief does not have a number for it. Poorly soluble drugs are dispersed in polymer matrices as glasses because the amorphous form dissolves faster, and shelf life is set by keeping storage far enough below T_g that molecular mobility is negligible. The research pass for this brief could not retrieve the review literature that would let it state how many marketed products this covers, so it states none.

Frontier Colloidal physics is not merely adjacent; it supplies most of the experimental evidence in this brief. Every direct measurement of a point-to-set length, a facilitation volume or a cooperatively rearranging region reported here was made on colloids, because they are the only glass-formers whose individual constituents can be watched. The transferability of those conclusions to molecular liquids is an assumption the field makes and does not test.

Speculative Two neighbours on this map share the underlying question without owning it. Quantum Materials is the nearest existing brief and is about solids whose behaviour comes from electronic correlation, disorder and device yield; it treats reproducible synthesis as the binding constraint, which is the same constraint seen from the crystalline side. Biomolecular Condensates touches glassy ageing in protein-rich droplets, where the liquid-to-gel-to-solid progression is described in similar language. Neither owns the transition itself and this page does not duplicate them.

Speculative The sibling commissioned alongside this brief is the sharpest case in the whole subject. Supercooled Water Anomalies covers a liquid whose supercooled behaviour is anomalous in more than seventy measured ways and whose glass-forming properties have been argued to require a second critical point. Water is the standing counterexample to any claim that one theory covers all glass-formers, and the fragile-to-strong crossover claimed for water is the same class of claim that better viscometry deleted in chalcogenides in 2025.

Frontier The field’s institutional form is the topical collaboration, and the flagship one has visibly wound down. The Simons Collaboration on Cracking the Glass Problem organised much of the theoretical work of the last decade; its public publications listing, as retrieved for this brief, runs from 2016 to 2019 and lists nothing more recent. Whatever the collaboration’s present status, a programme whose public record stops seven years before the brief is written is not the vehicle carrying the next result.

Speculative The institutional requirement this subject actually has is an adjudication venue, and no discipline routinely provides one. Physics has review articles, which restate positions, and conferences, which host both. What it does not have is a standing body that records what each theory predicted for a named measurement before the measurement was made. Astronomy and particle physics build this into their instrument proposals; condensed matter does not, and the cost is visible in a dispute that has absorbed every decisive result of the last fifteen years.

Established The metrological institutions exist and are not being used. National measurement institutes maintain viscosity standards; the glass-physics literature reports viscosities across seventeen decades without a shared uncertainty budget. A fragile-to-strong crossover that survived in the literature until 2025 on the strength of one technique’s systematic error is the argument for closing that gap, and it is the same argument made in Metrology Infrastructure.

Handwave Funding structure quietly favours the stalemate. Both programmes are productive, both publish in strong venues, and a proposal to run the adjudicating experiment is a proposal whose most likely outcome is that someone loses. That is an unattractive thing to write on a grant application and an attractive thing for a field to have done. No funder has offered the instrument, which would be a small coordinated call rather than a facility.

Established The direct ethical surface of this subject is small and the indirect one runs through medicine. Nothing about measuring a correlation length in glycerol harms anyone. But the shelf life of an amorphous drug product is set by a rule of thumb about storage temperature relative to T_g, and the confidence in that rule rests on an extrapolation of the same curve whose shape the field cannot derive. Where the extrapolation fails, the failure appears as recrystallisation in a product on a shelf.

Speculative The claim most in need of a flag is the cryopreservation one, and it is not this page’s to make. Vitrification has demonstrably preserved a rat kidney for 100 days with restored function after transplantation. Statements extending that to human organs, to whole bodies, or to information-theoretic preservation of a brain are claims of a different order and are examined in Cryonics and Brain Preservation. What this brief contributes is the underlying physics: the margin between vitrification and nucleation is narrow, temperature-dependent and not predictable from first principles.

Frontier The integrity question in this field is about absorbing evidence rather than about fabricating it. There is no scandal here of the kind that Quantum Materials records for room-temperature superconductivity. What there is instead is a slower failure mode: results that ought to be decisive are reinterpreted rather than conceded, and the reinterpretations are published, peer-reviewed and often correct. Distinguishing legitimate theory development from indefinite retreat is a judgement call that the field currently makes case by case and in private.

Speculative Machine learning introduces a specific epistemic risk here. A model that predicts particle mobility at 0.85 correlation without naming the structural feature it used is, from the point of view of the theoretical dispute, a very good oracle and no evidence at all. The risk is that predictive success is read as explanatory success, and the roadmap literature is explicit that it should not be. Philosophy of Science carries the general form of that argument.

Handwave The distributional question is narrow and worth stating anyway. If the deposition window for ultrastable glasses becomes predictable, the benefit accrues to firms with deposition capacity — display, semiconductor and specialty-coating manufacturers. The knowledge is publishable and the capital is not, which is the shape Technological Sovereignty examines in general.

Established Glass is already load-bearing for civilisation, and a theory of the glass transition would not make it more so. Windows, containers, optical fibre, laboratory apparatus and the immobilisation matrix for high-level nuclear waste are all glasses, and all of them were engineered without a theory of why the material stops flowing. The civilisational implication of solving the problem is therefore not a new capability; it is the removal of a tax paid in qualification time, empirical scans and safety margins.

Speculative The largest plausible consequence is in materials qualification, and it is a change in speed rather than in kind. Every amorphous material — a metallic glass coating, a chalcogenide memory film, a polymer matrix, an amorphous drug dispersion — is currently qualified by ageing studies that take as long as they take. A predictive theory converts part of that into computation. The analogous shift in crystalline alloys is the subject of Additive Manufacturing Qualification, and the honest comparison is that qualification reform saves years per material, not orders of magnitude across an economy.

Speculative The second consequence is preservation, and it is the one where the stakes are asymmetric. Vitrification is how biological material is held outside time, and how radioactive waste is held outside the biosphere. Both are bets on the stability of a non-equilibrium state over durations nobody has observed. A theory that predicted the ageing of a glass would change the confidence interval on both bets, and the amber result — a glass whose low-temperature excitations were unchanged after 110 million years — is the only long-baseline datum the field has.

Handwave The third consequence is epistemic and applies beyond glasses. This is a problem in classical statistical mechanics, with no missing particles and no inaccessible energy scale, that has resisted a definitive answer for longer than most problems in fundamental physics. If the resolution is that the question was malformed — that strong and fragile liquids arrest for different reasons — that is a data point about how often unification is the right ambition, and it belongs beside the material in Scientific Revolutions.

Handwave The counterfactual is the honest close. If nobody solves the glass transition in the next fifty years, industry will continue depositing, annealing and formulating exactly as it does now, slightly better each decade through empirical scans and machine-learned surrogates. The cost of failure is a permanent tax, not a catastrophe, and any page claiming otherwise is selling something.

These horizons track what can be measured and computed, because there is no deployment programme here to track and the industrial uses of glass do not wait on the theory:

• 10 yr: Frontier Expect the three-dimensional equilibrium configurational-entropy computation to be attempted and probably completed, since it is a scaling-up of a published two-dimensional protocol rather than a new method. Speculative Expect soft pinning and nonlinear dielectric susceptibility to be applied to the same molecular liquid, and expect the first result to be ambiguous, because the two methods measure different proxies for the same length. Speculative Expect machine-learned predictors to saturate near the achievable correlation ceiling without resolving the dispute, and expect at least one paper claiming they have.
• 25 yr: Speculative This is the window in which the quantitative amorphous-order test of section 7 plausibly returns a number good enough to exclude one camp. Speculative The more likely outcome is a synthesis rather than a victory: excitations as the microscopic events, cooperative regions as their accumulated consequence, with the timescale separation reported in the colloidal work as the bridge. Handwave If the synthesis holds, the field will describe it as having been obvious all along, and the question of which theory was right will stop being asked rather than be answered.
• 50 yr: Handwave On this horizon the plausible development is predictive rather than explanatory: a validated route from composition to fragility and to a deposition window, delivered by a surrogate model that nobody can read. Speculative If that arrives without a theory, the practical problem is solved and the scientific one is abandoned, which is a specific and not uncommon way for a pre-paradigmatic subject to end.
• 100 / 250+ yr: Handwave Beyond useful forecasting. The defensible statement is about shape: a problem in classical statistical mechanics with no missing ingredient either yields to a better method or is eventually reclassified as a family of different problems, and both have precedents. Handwave Any specific claim about what a solved glass transition would enable at this range is an assertion, and this page does not make one.

• Depends on Nothing on this map blocks this subject, and the absence is informative. Quantum Materials is the nearest existing brief and supplies context rather than a prerequisite: it owns reproducible synthesis and device yield in crystalline and layered solids, where this page owns the amorphous state itself. Autonomous Materials Discovery develops the search machinery that would exploit a predictive theory but is not waiting on one, and Metrology Infrastructure supplies the measurement culture this field has not adopted.
• Requires (not on this map) Six conditions, in the order of the tokens above. The molecular length. A static amorphous-order length measured in a molecular glass-former across the last four decades of relaxation time, by soft pinning and by fifth-order dielectric susceptibility on the same sample; colloids have delivered the length without the decades and molecular liquids the decades without the length. The three-dimensional entropy. The equilibrium computation that put the Kauzmann temperature at zero in two dimensions, repeated in three, with finite-size scaling and three independent estimators. The deposition control. Rates near 1 nm per minute with substrate temperature held at fractions of T_g and substrate modulus as a controlled variable, at the film thicknesses over which surface-mediated equilibration reaches 170 nm. The falsification criterion. A written, pre-registered statement from each camp of what measured value it would concede to — the cheapest item on this list and the one with no constituency. The reference liquids. Certified viscosity standards and an interlaboratory comparison across capillary, parallel-plate and oscillating-cup techniques, after a one-decade systematic error manufactured a fragile-to-strong crossover that survived in the literature until 2025. The buyer. A customer for ultrastable films designed rather than scanned; the deposition industries exist, the demand for a predicted rather than an empirical process does not yet.
• Enables A predictive theory would shorten qualification for amorphous materials, which is the concrete consequence for Additive Manufacturing Qualification and for the immobilisation lifetimes assumed in Nuclear Waste Solutions, and would tighten the margin between vitrification and nucleation that Cryonics depends on. No typed enabling edge is claimed, because a theory that does not yet exist enables nothing on a schedule, and the industries above are already shipping without it.
• Adjacent Colloid science, nonlinear dielectric spectroscopy, chalcogenide memory, metallic glasses and cryobiology supply every number on this page. Within this map: Supercooled Water Anomalies for the one liquid that refuses to fit, Quantum Materials for the crystalline side of the synthesis problem, Biomolecular Condensates for glassy ageing in biology, Ultra-Efficient Computing Energy Systems for the memory technologies built on chalcogenide glasses, and Objective Collapse Models as the sibling case of a pre-paradigmatic subject where the argument is about which extensions count.

Established “Glass is a liquid that flows, which is why medieval windows are thicker at the bottom.” The viscosity of a vapour-deposited indomethacin glass has been measured at exapoise values — of order 10¹⁷ Pa s — against 10¹¹ to 10¹³ poise at the conventional glass transition, and window glass at room temperature is far below its transition. Flow at those viscosities over centuries is not observable, and the thickness variation in old window panes is a record of how the panes were made. The underlying idea, that a glass is a liquid that has fallen out of equilibrium, is correct; the inference about cathedrals is not.

Frontier “The glass transition is a phase transition.” As measured, it is not: T_g is defined by a viscosity of 10¹² Pa s and moves with cooling rate. Whether a genuine thermodynamic transition hides below it is the open question, and the most direct answer available — full equilibration of a two-dimensional atomistic glass to zero temperature — found the Kauzmann temperature extrapolating to zero in the thermodynamic limit, with no finite-temperature entropy crisis. That is evidence against a finite-temperature transition in two dimensions and silence about three.

Established “Ultrastable glass is just very old glass.” This is the misconception the anchor for this brief edges towards, and it is refuted by a single measurement. Amber hyperaged for 110 million years shows specific heats below one kelvin identical to its own annealed and rejuvenated samples: the two-level systems and the boson peak survived unchanged. Vapour deposition reaches states that ageing does not reach, and the equivalence between deposited stability and thousands of years of ageing is an equivalence in fictive temperature and density only.

Frontier “Swap Monte Carlo has disproved RFOT.” It has established that a change of kinetic rule buys twelve to thirteen orders of magnitude in relaxation time while leaving every static quantity fixed, which is a serious problem for any theory that derives the barrier from statics alone. The RFOT reply — that swap postpones the onset of glassy dynamics rather than lowering a thermodynamic barrier, by an argument from crumbling metastability with nucleation as the precedent — is published, specific and not obviously wrong. The claim of disproof outruns the evidence in both directions.

Frontier “The fifth-order dielectric experiment settled it for amorphous order.” It found compact domains with fractal dimension 3 and the predicted relation between fifth- and third-order susceptibilities in glycerol and propylene carbonate, and its authors describe this as strong support for thermodynamic amorphous order. It is two liquids, one technique, and a relation whose interpretation assumes part of the theory it supports. It is the best molecular evidence in the field and it is not a settlement.

Speculative “Dynamic facilitation predicts no static length.” This framing appears in commissioning documents including the one for this brief, and it is not what the theory says. Facilitation claims that a static length is not what controls the barrier; a length can grow without doing the work. The experimental record is consistent with that reading: the same colloidal system, studied by overlapping author groups, produced both a monotonically growing point-to-set length and a growing facilitation volume on approach to the same transition.

Frontier “Fragile-to-strong crossovers are an established feature of glass-formers.” In germanium–selenium chalcogenides they were not. Measurements across four compositions and three techniques spanning about thirteen decades of viscosity are described by a single steepness index, and the earlier crossover is attributed to the oscillating-cup method disagreeing with capillary and parallel-plate measurements by nearly one order of magnitude. Crossovers claimed in other systems, water included, are not thereby refuted — but they now carry a burden of instrumental proof they did not carry before 2025.

Handwave “Amorphous means structureless.” The 2026 review of colloidal vitrification concludes the opposite: excess entropy, point-to-set lengths, machine-learned softness, intermediate-range order and soft modes all link static structure to dynamics, provided the correlations considered extend well beyond the first neighbour shell. The reason glasses looked structureless for decades is that the field was looking at the first neighbour shell, which is where the two-body structure function puts its information and where the answer is not.

Handwave “One theory will turn out to be right.” This is the assumption the whole dispute rests on and it has no evidence behind it. The colloidal experiment that measured both excitations and cooperatively rearranging regions reported that both classes of theory are compatible with its data and suggested the two describe the same events at different resolutions. A synthesis, or a partition of the problem by material class, is at least as likely as a victory, and neither camp would call that a result.