arxiv: 2604.21109 · v1 · submitted 2026-04-22 · ❄️ cond-mat.dis-nn · cond-mat.mtrl-sci· cond-mat.soft

Recognition: unknown

The two-level systems in cryogenic solids, or how to avoid stressful memories

Vassiliy Lubchenko

Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:05 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mtrl-scicond-mat.soft

keywords two-level systemsstructural glassesconfigurational entropyultrastable glassesambervapor depositionlow-temperature excitationscryogenic solids

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The pith

Two-level systems persist in amber because its stability comes from bonding, not entropy reduction like in vapor-deposited glasses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper addresses why some enthalpically stable glasses show fewer two-level systems than conventional melt-quenched ones, while ancient amber does not. It states that any depletion of TLSs indicates lower configurational entropy relative to bulk-quenched glasses, as occurs in vapor-deposited films and swap Monte Carlo samples. Amber achieves its stability through increased bonding over geological time rather than through ageing-induced entropy reduction, allowing TLSs to remain. This resolves the observations and points to distinct paths to stability with different impacts on low-energy excitations. The author also notes discrepancies in existing predictions for TLS cooperativity and proposes targeted experiments.

Core claim

A depletion of the TLSs, if any, means the configurational entropy of the material is lower than that of conventional glasses made by bulk-quenching a melt. Ageing does induce reduction in configurational entropy, but amber, we speculate, achieves enthalpic stabilization through increased bonding, not ageing.

What carries the argument

The distinction between configurational entropy reduction, which depletes TLSs, and enthalpic stabilization via increased bonding, which preserves them.

If this is right

Vapor-deposited and swap Monte Carlo glasses exhibit TLS depletion because their configurational entropy lies below that of melt-quenched material.
Amber's retained TLSs indicate its stability does not involve the same entropy reduction seen in other ultrastable solids.
Different preparation routes to enthalpic stability produce different densities of low-energy excitations.
Existing models of TLS cooperativity disagree and require experimental resolution to align with observed depletion patterns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Materials designers could select stabilization methods to control TLS density for cryogenic or quantum applications.
The bonding-versus-entropy distinction may extend to other long-term stabilized amorphous solids beyond amber.
If bonding increases dominate in amber, related changes in mechanical or density properties could be tested against entropy-reduced glasses.

Load-bearing premise

That a reduction in TLSs directly signals lower configurational entropy than in melt-quenched glasses, and that amber's enthalpic stability arises specifically from bonding rather than ageing.

What would settle it

Direct measurement of configurational entropy in amber versus vapor-deposited and melt-quenched glasses; if amber shows entropy equal to conventional glasses despite its stability and TLS persistence, the bonding mechanism is supported.

Figures

Figures reproduced from arXiv: 2604.21109 by Vassiliy Lubchenko.

**Figure 1.** Figure 1: The equilibrium equation of state (EOS) of a substance in the enthalpy range pertinent to liquidcrystal coexistence. The thick blue line depicts the liquid entropy as a function of enthalpy, the thick black line the entropy of the crystal. The solid portion of the liquid EOS corresponds to the ergodic regime T > Tcr, the dashed portion signifies ergodicity is broken on times less than the structural relax… view at source ↗

**Figure 2.** Figure 2: Signatures of depletion in the number of two-level systems in (a) ultrastable glasses [21] and (b) model Lennard-Jones mixtures [22]. quenching rate logarithmically weakly [25]. The range of rates practically achievable by thermal quenching is determined by the thermal conductivity of the substance and is not particularly broad, in the first place. One may expect that the density of states for the TLSs sho… view at source ↗

**Figure 3.** Figure 3: Suppose that the activation energy for inter-minimum transitions is significantly greater than temperature, so that the characteristic rate 1/τc for these transitions is 5 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 3.** Figure 3: Graphical explanation of ergodicity breaking. p(x) stands for the probability distribution of the variable x. Note that we have not included the additive contribution −T svib of the vibrational entropy to the free energies G1, G2, and G, for clarity. This contribution is the same for all three free energies. much lower than the rate of vibrational relaxation 1/τvib. On times such that τvib < t < τc, the vi… view at source ↗

**Figure 4.** Figure 4: When drawing Fig. 4, we assumed there were two DSC peaks for concreteness. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 4.** Figure 4: Main graph (left): Sketch of the enthalpy dependence of the entropy for a liquid that allows for two low-enthalpy phases that exhibit local ordering; these two phases are labelled “ordered” USG. “USG”=“ultrastable glass”. “EOS”=“equilibrium equation of state.” The corresponding down-scan (blue dashed) and up-scan for DSC are sketched in the auxiliary graph on the right. Note the respective slopes of the tw… view at source ↗

**Figure 5.** Figure 5: Temperature dependence of the degree cooperativity for (a) α-relaxations and (b) β-relaxation. From Ref. [22]. cesses are non-compact, string-like. For these, the cooperativity, in contrast, increases with temperature. We show both of these trends in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: Diagrams juxtaposing equilibrium and off-equilibrium behaviours of a liquid. were steady. We first note that the pristine, matured amber is about 2% denser than the same material after annealing [23]. The contraction could have resulted from a combination of two distinct processes. One is a contraction caused by the polymerization-induced increase in bonding. The contraction is largely uniform, even though… view at source ↗

read the original abstract

Structural glasses prepared by bulk quenching a liquid melt universally exhibit puzzling low-energy excitations commonly known as the ``two-level systems'' (TLSs). Recent studies indicate that ultrastable glassy films made by vapor deposition exhibit substantially fewer TLSs and, at the same time, are more stable enthalpically than conventional glasses made by quenching a melt. A similar phenomenon is observed in very stable glasses of model liquid mixtures prepared using swap Monte Carlo sampling. However, in a separate set of enthalpically stable solids, exemplified by amber matured over geological times, the two-level systems persist. In addressing this seeming conflict, we emphasize that a depletion of the TLSs, if any, means the configurational entropy of the material is lower than that of conventional glasses made by bulk-quenching a melt. Ageing does induce reduction in configurational entropy, but amber, we speculate, achieves enthalpic stabilization through increased bonding, not ageing. We separately comment on the discrepancy among existing predictions for the extent of cooperativity of the two-level systems. Several experiments are suggested to test the present picture.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper offers an interpretive split between entropy-driven TLS depletion in vapor-deposited and swap-MC glasses versus bonding-driven stability in amber, but the TLS-entropy link stays qualitative.

read the letter

The paper's main point is that depletion of two-level systems in ultrastable glasses signals lower configurational entropy than in ordinary melt-quenched glasses. Amber, despite being enthalpically stable, keeps its TLSs because its stability comes from increased bonding rather than from the entropy reduction that ageing produces. This distinction organizes the conflicting reports: vapor-deposited films and swap-Monte-Carlo glasses show fewer TLSs and are interpreted as having lower entropy, while amber does not. The text also notes varying predictions for TLS cooperativity and lists experiments that could test the overall view. The strength is in spotting that not all routes to stability are equivalent at the level of low-energy excitations. Treating amber separately avoids lumping every stable glass into one category and points to bonding as an alternative stabilization mechanism. The soft spot is the absence of a derived relation between TLS density and configurational entropy. The argument treats the connection as logical inference from prior work, yet TLS density depends on barrier and asymmetry distributions while entropy counts inherent structures; these can vary independently. The amber claim is presented as speculation without a specific bonding metric or direct comparison to ageing in similar materials. Readers in condensed-matter glass physics who track low-temperature anomalies and ultrastable solids will get the most from it. The piece is short and focused, so it could fit a perspective format. It deserves peer review because the tension it addresses is genuine and the proposed tests are concrete, even though the central mapping would need more support to hold up under scrutiny.

Referee Report

2 major / 0 minor

Summary. The manuscript synthesizes literature on two-level systems (TLS) in structural glasses, claiming that depletion of TLS in ultrastable glasses (vapor-deposited films or swap Monte Carlo samples) indicates lower configurational entropy than in melt-quenched glasses, while speculating that amber's enthalpic stability arises from increased bonding rather than ageing; it also comments on TLS cooperativity discrepancies and proposes experiments to test the picture.

Significance. If the proposed interpretive framework holds, it offers a unifying perspective reconciling TLS observations across preparation methods and distinguishes entropy reduction from other stabilization routes, with the suggested experiments providing concrete falsifiable tests. The paper's strength lies in its synthesis of independent prior observations without introducing new fitted parameters or self-referential equations.

major comments (2)

[Abstract] Abstract: The central claim that 'a depletion of the TLSs, if any, means the configurational entropy of the material is lower' lacks a quantitative derivation or explicit mapping from TLS density (set by low-energy barrier distributions) to configurational entropy S_c (set by the number of inherent structures); these quantities can in principle decouple if barrier heights or asymmetry statistics vary independently of landscape multiplicity.
[Abstract] Abstract: The speculation that amber achieves enthalpic stabilization through increased bonding (rather than ageing) is presented without a specific bonding metric, quantitative comparison to ageing-induced changes, or reference to a particular section deriving this distinction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We appreciate the positive assessment of the paper's synthesis of TLS observations across preparation protocols. We address each major comment below and will make revisions to improve clarity and precision.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that 'a depletion of the TLSs, if any, means the configurational entropy of the material is lower' lacks a quantitative derivation or explicit mapping from TLS density (set by low-energy barrier distributions) to configurational entropy S_c (set by the number of inherent structures); these quantities can in principle decouple if barrier heights or asymmetry statistics vary independently of landscape multiplicity.

Authors: We agree that the manuscript does not provide a new quantitative derivation mapping TLS density directly to configurational entropy, as the work is an interpretive synthesis of existing literature rather than a theoretical calculation. The statement is motivated by the standard potential-energy-landscape picture in which TLS correspond to tunneling transitions between nearby inherent structures; a reduction in the density of such low-barrier excitations is therefore expected to reflect a lower multiplicity of accessible low-energy states. While we acknowledge that barrier-height or asymmetry distributions could in principle vary independently of the total number of inherent structures, the empirical correlation observed in ultrastable glasses (vapor-deposited films and swap-MC samples) supports the interpretive link. To address the concern, we will revise the abstract to replace the phrasing with 'is consistent with a lower configurational entropy' and will add a concise paragraph in the main text (with appropriate references to landscape studies) that explicitly notes the absence of a strict one-to-one mapping and the possible role of barrier statistics. revision: yes
Referee: [Abstract] Abstract: The speculation that amber achieves enthalpic stabilization through increased bonding (rather than ageing) is presented without a specific bonding metric, quantitative comparison to ageing-induced changes, or reference to a particular section deriving this distinction.

Authors: The distinction drawn for amber is indeed presented concisely and is speculative. It rests on the key observation that TLS remain abundant in amber despite its high enthalpic stability, in contrast to the TLS depletion seen in other ultrastable glasses. In the body of the manuscript we cite literature indicating that amber undergoes slow chemical evolution (cross-linking, oxidation) that strengthens intermolecular bonding over geological time, thereby lowering enthalpy without the same reduction in configurational-state multiplicity that accompanies physical ageing. We accept that the abstract lacks an explicit metric or cross-reference. We will therefore revise the abstract to include a brief parenthetical reference to the relevant discussion section and will add one or two additional citations to studies that quantify bonding changes in aged resins. Because the claim remains interpretive and no new quantitative data are introduced, we will keep the language as a hypothesis rather than a definitive conclusion. revision: partial

Circularity Check

0 steps flagged

No circularity in derivation chain; claims are interpretive synthesis of external observations

full rationale

The paper's central statements equate TLS depletion with lower configurational entropy and attribute amber stability to bonding rather than ageing, but these are presented as logical inferences from cited experimental results on vapor-deposited films, swap Monte Carlo glasses, and geological amber. No equations, fitted parameters, or self-citations are used to derive these equivalences; the text contains no self-referential definitions, predictions that reduce to inputs by construction, or load-bearing uniqueness theorems from the author's prior work. The argument remains self-contained against external benchmarks and does not reduce any result to its own premises.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The argument relies on the standard but unproven domain assumption that TLS density directly tracks configurational entropy; no free parameters, new entities, or additional axioms are introduced.

axioms (1)

domain assumption Depletion of TLSs implies lower configurational entropy than in bulk-quenched glasses
This equivalence is asserted without derivation or quantitative mapping in the abstract.

pith-pipeline@v0.9.0 · 5492 in / 1177 out tokens · 41070 ms · 2026-05-09T22:05:54.644635+00:00 · methodology

discussion (0)

Reference graph

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