{"id":"b48f5d4d-af2c-4e0a-9a84-7ddc0fbe3997","arxiv_id":"2607.15920","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In a simulated glass former, large temperature up-jumps are best described by a separate material time for each observable, with the mean-square displacement gaining the most.","lead":"This paper tests whether giving each measured property its own \"material clock\" better describes how a simulated glass relaxes after large temperature jumps. For the three properties studied, each property's own clock gives the best collapse, but the gain is large only for the mean-square displacement.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"For Cuu and ISF, 'own material time best' may be an in-sample artifact: Eq. (5) requires the triangular relation, which is violated ~2.3–5.6× noise; ξ_A is then a-dependent and fitted to the same data being collapsed.","rationale":"The paper's strongest claim is that each observable has its own material time. The load-bearing assumption is that Eq. (5) is a legitimate construction, i.e., that the triangular relation holds closely enough that ξ_A is unique and not merely a fit parameter. For the MSD this is supported by the data. For Cuu and the ISF, however, the measured violations are 2.3 and 5.6 times the equilibrium noise level; the paper explicitly leaves the threshold for 'large' open. These are exactly the cases where the collapse improvement is modest and where the choice of a changes the collapse qualitatively (Appendix C). The comparison in Fig. 6 therefore risks circularity: ξ_A is constructed from A's own autocorrelation and then shown to collapse A better than ξ_B. This would happen even for a system with a single universal material time, as long as statistical noise or small triangular violations exist, because the construction absorbs those fluctuations into ξ_A. A cross-validation split of the 50 independent simulations would settle this: if the own-clock advantage for Cuu and ISF persists on held-out data, the claim is real; if not, the universal material time remains adequate and the paper's conclusion is an overfitting artifact. I therefore keep the conditional verdict: the MSD result is solid and novel, but the general claim 'for all properties' requires the out-of-sample test.","tokens_in":16022,"tokens_out":5005,"duration_ms":57361,"concrete_test":"Split the 50 independent runs into two disjoint halves (e.g., 25+25). Construct ξ_A for A=Cuu, F_s, MSD on half 1 only, using the paper's iterative procedure; evaluate the collapse measure col[f](ξ_A) for all f on half 2. Repeat with halves swapped. If for Cuu and F_s the own-material-time advantage disappears or falls within the run-to-run spread, the headline claim is an in-sample artifact. Also, for a representative a, report the full 3×3 matrix col[f](ξ_A) with bootstrap uncertainties; if the ranking 'own is best' is not robust to a, the claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV defines ξ_A via Eq. (5) by requiring C_A(t1,t2)=φ_A_eq(ξ_A(t2)−ξ_A(t1)), constructed iteratively from the single observable A. This is a valid clock only if the triangular relation (Eq. 4) holds; otherwise ξ_A depends on the arbitrary threshold a and on the chosen ladder of times. The paper's own Fig. 2(d-e,g-h) reports that after the large 0.37→0.48 jump the per-pixel standard deviation of C_13 reaches 2.3 and 5.6 times the equilibrium-noise maximum for C_uu and F_s, respectively, and the text concedes 'what is to be regarded as a \"large\" deviation ... is debatable.' Appendix C shows that col[f](ξ1) changes qualitatively with a (monotonic vs oscillating). In this situation the comparison in Fig. 6 — collapse of A under ξ_A vs under ξ_B — is not a fair test: ξ_A has been fitted to A's own two-time function, so A will tend to collapse best under ξ_A even if no property-specific clock exists. The central claim that 'for all properties the data collapse best' is therefore only secure for the MSD, whose triangular relation violations stay at the equilibrium baseline. Without an out-of-sample or cross-validated comparison, the Cuu and ISF results do not establish a property-dependent material time.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses simulation data from large temperature up-jumps in a binary Lennard-Jones mixture to test whether assigning a separate 'material time' to each observable improves data collapse compared with a universal Tool-Narayanaswamy time. The authors examine the potential-energy autocorrelation, the self-intermediate scattering function, and the mean-square displacement. They verify the Cugliandolo-Kurchan triangular relation for each observable, iteratively construct a material time for each property using a threshold decorrelation value a, and compare collapses with an L2-based metric. They report that each property collapses best under its own material time, most strongly for the MSD, and conclude that material times are property-dependent.","tokens_in":16433,"tokens_out":5879,"duration_ms":63382,"significance":"The question of whether the Tool-Narayanaswamy material time is universal or property-dependent is important for the physics of aging. The paper provides a transparent and detailed analysis of triangular-relation violations, including heat maps, standard-deviation distributions, and complementary cumulative distribution functions, and introduces a clear collapse metric. The MSD result—where the triangular relation holds within equilibrium noise and the improvement from the own material time is substantial—is a valuable positive finding. However, the claim of property-dependent material times for all three observables is weakened by the in-sample nature of the comparison and by the threshold dependence of the construction for the potential-energy autocorrelation and the ISF. As it stands, the paper is stronger as a diagnostic study than as a demonstration of property-dependent clocks.","major_comments":[{"comment":"The comparison 'own material time best' is partly tautological. Since ξ_A is constructed from C_A itself via Eq. (5), which imposes C_A(t1,t2)=φ_A_eq(ξ_A(t2)-ξ_A(t1)), the collapse of A under ξ_A is enforced by construction whenever the triangular relation holds. The observation that col_A(ξ_A)<col_A(ξ_B) therefore mainly measures the degree of triangular-relation violation and the sensitivity of ξ_A to the arbitrary threshold a, not an independent physical fact. To support the abstract's claim for all three properties, an out-of-sample test is needed—for example, constructing ξ_A on one subset of the 50 simulations and testing collapse on the remaining subsets—or a direct test of whether ξ_A(t)/ξ_B(t) is constant. Without such a test, the result for Cuu and ISF is not secure.","section":"§IV–V, Eq. (5), Fig. 6"},{"comment":"For C_uu and F_s after the T=0.37→0.48 jump, the per-pixel standard deviation reaches 2.3 and 5.6 times the equilibrium noise, and the text concedes that 'what is to be regarded as a \"large\" deviation ... is debatable.' This concession is load-bearing because Eq. (5) defines a unique material time only when the triangular relation Eq. (4) holds; otherwise ξ_A depends on the chosen a and on the time ladder, as Appendix C shows. The authors should either restrict the main claim to the MSD (where violations stay at the equilibrium baseline) or provide a statistical criterion for what counts as an acceptable violation. The current conclusion that 'the triangular relation is obeyed to a good approximation' for all three properties is too permissive for Cuu and ISF.","section":"§IV, Fig. 2(d-e,g-h)"},{"comment":"The collapse measure and the claim 'the best collapse is always obtained' need an error assessment. Figure 6 shows that the improvement is not always sizable and is 'occasionally worse' at some ξ_1 values; Appendix C further shows that for small a the collapse curves become oscillatory. Without error bars or a paired statistical comparison across the 50 independent simulations, the statement that 'for all properties' the own material time is best is not quantitatively supported, especially in the intermediate-ξ_1 regime where the collapse behavior is most informative.","section":"§V, Eq. (6), Fig. 6"}],"minor_comments":[{"comment":"Cugliandolo and Kurchan's 1994 paper is cited twice, as Ref. [39] and Ref. [44], with identical bibliographic details. Please merge or distinguish them.","section":"References"},{"comment":"Minor grammar issues: 'was recently shown to becomes less effective' in the abstract; 'Not that while we here regard...' should be 'Note that while we here regard...' in Section III.","section":"Abstract and Introduction"},{"comment":"The caption labels panels '(d,e,h)' and then '(d-f)' and '(g-i)' inconsistently. Please align the panel references with the actual layout.","section":"Figure 2 caption"},{"comment":"The choice a=0.1 for ξ_u and ξ_ISF and a=0.75 for ξ_MSD is made to achieve comparable material-time units, but the authors state this choice does not give the very best collapse. This sensitivity to a is discussed in an appendix; a brief statement in the main text would help readers weigh the robustness of Fig. 6.","section":"§IV, threshold choice"},{"comment":"The exclusion of the dynamic susceptibility and non-Gaussian parameter is justified in one sentence. A slightly longer explanation of why non-monotonicity prevents a well-defined material-time mapping would be helpful.","section":"§I, non-monotonic observables"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reports a careful simulation analysis from an established group, and the MSD result is a solid positive contribution. The central claim about all three observables is, however, weakened by the in-sample construction of the material times and by the acknowledged triangular-relation violations for C_uu and F_s. These issues are fixable with an out-of-sample test or a more modest framing, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper does something useful: it takes the idea of property-dependent material times, which the same group floated in Ref. 31, and gives it a concrete quantitative test for large temperature up-jumps. For each of three observables — potential-energy autocorrelation, self-intermediate scattering function, and mean-square displacement — they construct a material time using an iterative threshold procedure and then ask which clock best collapses each observable's aging curves. The headline result, that each property collapses best in its own material time, is most convincing for the MSD, where the triangular relation holds within noise. That is a real, incremental finding.\n\nWhat is well done: the triangular-relation analysis is detailed and honest, with equilibrium noise baselines; the authors transparently show in Appendix C that the decorrelation threshold a changes the collapse behavior, and they concede that \"large\" deviations are debatable. The citation pattern is appropriate; the heavy reliance on their own Ref. 31 is natural for a follow-up.\n\nThe soft spot is the in-sample issue. The material time ξ_A is defined via Eq. (5) as the reparametrization that makes C_A match its own equilibrium function, so the observation that C_A collapses best under ξ_A is partly circular. For the MSD, the triangular-relation test rescues it: since the relation holds, the construction is not merely fitting noise. For Cuu and the ISF after the largest jump, the triangular relation is violated at up to 2.3–5.6 times equilibrium fluctuations, and the a-dependence can qualitatively change col[f]. In that regime the comparison in Fig. 6 is not a fair out-of-sample test. The claimed improvement for those two observables is suggestive but not secure. Also, no error bars are given on the collapse measure, and no code or data are shipped.\n\nWhat would fix it: an out-of-sample or cross-validated construction of ξ_A (e.g., from a subset of trajectories or waiting times, then test on the rest), or a fixed reference clock, plus error bars. The MSD result would likely survive; the Cuu/ISF claims might not.\n\nWho this is for: people working on Tool-Narayanaswamy theory, aging simulations, and time-reparametrization invariance. It is a within-field correction with a plausible, partially supported claim. I would send it to a serious referee, not desk reject, because the triangular-relation analysis is a useful contribution and the MSD result is likely robust. I'd ask for the additional out-of-sample analysis before accepting.","headline":"A careful, honest simulation study showing that property-specific material times — especially for the MSD — improve collapse of aging data after large up-jumps, though the Cuu and ISF comparisons are partly in-sample.","tokens_in":16840,"tokens_out":3612,"would_cite":true,"duration_ms":35721,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"After large temperature up-jumps, each aging observable in a glass-forming liquid collapses best when time is reparameterized by that observable's own material time, not by a single universal clock.","keywords":["physical aging","material time","TN formalism","triangular relation","temperature up-jump","binary Lennard-Jones mixture","mean-square displacement","time reparametrization"],"falsifier":"An even larger up-jump (e.g., from T=0.34 to T=0.48) or a new observable could test the claim: if the triangular-relation violations for the MSD grow beyond equilibrium noise and the MSD's own material time no longer yields the best collapse, the central claim fails. More concretely, if the ranking of collapse qualities changes when the decorrelation level a is varied within a reasonable range, the existence of a single 'own' best material time is called into question.","tokens_in":15936,"feed_emoji":"⏱️","tokens_out":6782,"duration_ms":69005,"temperature":0.7,"pith_summary":"Physical aging after a large temperature up-jump in a glass-forming liquid is not captured by one universal material time. This paper analyzes three two-time correlation functions—the potential-energy autocorrelation, the self-intermediate scattering function, and the mean-square displacement (MSD)—from simulations of a binary Lennard-Jones mixture subjected to up-jumps ending at T=0.48. For each observable, the authors construct a 'material time' from that observable's own decaying correlation and measure how well aging curves collapse onto the equilibrium master curve. The finding: every property collapses best when plotted against its own material time. The improvement is most pronounced for the MSD, which also satisfies the triangular relation within numerical uncertainty; the other two observables show deviations from that relation after the largest jump, and their improvement is modest.","feed_headline":"No single clock ages glass after big jumps","feed_subtitle":"Each observable collapses best with its own material time; MSD benefits most.","key_machinery":"The triangular relation (C_A(t1,t3) as a function of C_A(t1,t2) and C_A(t2,t3)) is the necessary condition for defining a material time from a two-time autocorrelation function: it guarantees that the correlation is determined by the material-time difference. The paper also employs the iterative construction of ξ_A from the condition that a fixed decorrelation level a corresponds to one unit of material time, and an L2-norm based collapse measure col[f](ξ1) that compares aging curves with the equilibrium curve at the same material-time difference.","core_discovery":"The paper's central claim is that the aging response following large temperature up-jumps is property-dependent: no single material time can collapse all observables, so each two-time function should be assigned its own clock. The material time ξ_A for observable A is defined by requiring C_A(t1,t2) = φ_A_eq(ξ_A(t2)-ξ_A(t1)), where φ_A_eq is the equilibrium correlation function; this requires the triangular relation to hold during aging. The authors test the triangular relation via pixel-binned statistics and find it obeyed within noise for the MSD, while the potential-energy autocorrelation and the intermediate scattering function show deviations up to 2.3 and 5.6 times the equilibrium stan","pith_inferences":["If property-dependent clocks hold generally, experiments that simultaneously monitor two observables during a large up-jump (e.g., enthalpy and volume) should reveal different material times; detecting such differences would confirm the multi-clock picture.","The special status of the MSD hints that a clock defined from the slowest particles—e.g., a 'harmonic inherent MSD'—might collapse other observables even better; this is a natural testable extension.","The observed sensitivity to the choice of a suggests that material time is not uniquely defined; an automated optimization of a to minimize col[f] would make the concept more predictive, but this goes beyond the paper."],"forward_implications":["The single-universal-material-time assumption (the TN formalism) has limited validity for large temperature up-jumps; property-specific clocks extend the aging description.","The mean-square displacement is the most reliable observable for defining a material time: it obeys the triangular relation best and collapses best under its own reparameterization.","The triangular relation provides a practical, quantitative test for whether an observable can be assigned a meaningful material time during aging.","Material-time definitions depend on the chosen decorrelation level a; an explicit specification of a is needed for reproducibility.","The results motivate exploring spatially resolved 'local clocks' as an alternative route to improving collapse for large jumps."],"fun_headline_variants":["Aging glass: each observable ticks its own clock","No universal material time for glass","MSD demands its own clock in aging glass","One material time per observable, best collapse","Property-specific clocks beat one glass clock"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The triangular relation is assumed to hold closely enough during aging for each observable to define a material time; for the potential-energy and scattering functions after the largest jump the deviations reach 2.3 to 5.6 times the equilibrium noise, and the paper does not specify how large a deviation still allows a meaningful material time.","fun_headline_variants_meta":{"raw":{"variants":["Aging glass: each observable ticks its own clock","No universal material time for glass","MSD demands its own clock in aging glass","One material time per observable, best collapse","Property-specific clocks beat one glass clock"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000246,"raw_usage":{"total_tokens":1369,"prompt_tokens":728,"completion_tokens":641,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":472,"completion_tokens_details":{"reasoning_tokens":575}},"tokens_in":472,"tokens_out":641,"duration_ms":7376,"temperature":1.0,"reasoning_tokens":575,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T21:54:24.892859+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An even larger up-jump (e.g., from T=0.34 to T=0.48) or a new observable could test the claim: if the triangular-relation violations for the MSD grow beyond equilibrium noise and the MSD's own material time no longer yields the best collapse, the central claim fails. More concretely, if the ranking of collapse qualities changes when the decorrelation level a is varied within a reasonable range, the existence of a single 'own' best material time is called into question.","supporting_citations":[],"review_version":1}