{"id":"e9ef1413-fb31-4565-bbb9-a57f0964fe56","arxiv_id":"2608.11073","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Above yielding, cyclically driven amorphous solids become irreversible through rare branching events caused by competition between nearly degenerate plastic instabilities, not through chaotic sensitivity to initial conditions.","lead":"This paper tests whether cyclically sheared amorphous solids become irreversible through chaos, and finds they do not: nearby trajectories stay locally stable and separate only through rare branching events. The authors trace these branching events to competition between nearly equal plastic instabilities, offering a mechanism for the reversibility irreversibility transition in driven disordered materials.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Microscopic mechanism claim rests on a soft-spot model with explicit stochastic branching (p_ir=0.01); particle simulations have not directly observed the proposed instability competition.","rationale":"The reader's weakest assumption is spot-on: the microscopic mechanism is extracted from a model with an explicit stochastic branching injection. I reviewed the Supplementary Material and confirmed the p_ir=0.01 rule. This is indeed a serious concern, because the model's branching statistics are perhaps not emergent. The particle simulations provide evidence for branching and for local stability, but they do not resolve the soft-spot competition; so the claim that 'branching originates from competition between nearly-degenerate plastic instabilities' is a model-based inference. The load-bearing test would be to look for such competition directly in the particle simulations. If absent, the central claim's 'microscopic origin' part would be weakened, though the no-chaos conclusion might still hold. I believe CONDITIONAL remains the correct verdict: the paper should be accepted only if the mechanism is verified in the particle system or if the model's p_ir dependence is shown to be irrelevant. No stronger rejection is warranted because the primary dynamical observation (no sustained chaos) is well supported.","tokens_in":13691,"tokens_out":6840,"duration_ms":60682,"concrete_test":"In the particle-based AQS simulations, apply a soft-spot detection method (e.g., localized vibrational modes or local yield stress mapping) to the configuration immediately before each branching event, and compute the distance-to-instability x_i (Eq. 7) for all soft spots in both the reference and perturbed trajectories. Test whether the first divergence corresponds to the activation of a nearly-degenerate pair of soft spots whose ordering is flipped by the perturbation (|Δ| close to zero). Survey at least 50 independent branching events. If no such swap is observed, the instability-competition mechanism is an artifact of the soft-spot model's p_ir injection rather than the physical mechanism.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim has two components: (i) post-yield trajectories are locally stable and irreversibility arises from rare branching events rather than sustained chaos, and (ii) the microscopic origin of branching is competition between nearly-degenerate plastic instabilities. Component (i) is directly supported by the particle-based AQS simulations (Fig. 1b, 2a), which contain no injected randomness. Component (ii) is inferred almost entirely from the mean-field soft-spot model. That model, however, contains an explicit stochastic branching source: the Supplementary Material states that 'whenever the dynamics reaches a system-wide configuration that has not been visited previously, a competing soft spot is added with probability p_ir = 0.01.' Without this injection, the model always reaches a limit cycle. Thus the exponential waiting-time statistics and the power-law branching rate could be direct consequences of this Poisson-like injection process rather than of the natural distribution of thresholds or an emergent instability-selection competition. The paper does not report how the branching rate depends on p_ir, and it does not demonstrate the predicted competition event in the particle simulations, which have no p_ir. If the model's branching statistics are controlled by p_ir, the claim that instability-competition is the generic microscopic mechanism is unsupported; the particle simulations only establish that branching occurs, not why.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies athermal quasistatic oscillatory shear of a two-dimensional Kob-Andersen glass and a mean-field soft-spot model. Using direct perturbation experiments, the authors report that post-yield trajectories do not exhibit sustained exponential divergence: typical perturbations decay, and irreversibility instead occurs through rare branching events with exponentially distributed waiting times, after which the separation grows diffusively. The soft-spot model reproduces the branching statistics, and by tracking soft-spot activations the authors attribute branching to competition between nearly-degenerate plastic instabilities, where a small perturbation changes which instability activates first and thereby rearranges the subsequent sequence of plastic events. The paper concludes that instability-selection-induced branching, rather than chaos, is the dynamical mechanism for irreversibility.","tokens_in":13913,"tokens_out":7525,"duration_ms":72399,"significance":"The central observational claim—that post-yield AQS trajectories are locally stable and that irreversibility arises through rare branching events—is direct, well-posed, and supported by the particle simulations, which contain no injected stochastic source. The verification that the post-branching separation diffuses with S ≈ 8D provides a quantitative and falsifiable check. If the microscopic mechanism claim is also sustained, the paper would provide a valuable bridge between deterministic dynamics and stochastic descriptions of the irreversibility transition. The main weakness is that the proposed instability-competition mechanism is demonstrated almost entirely in a soft-spot model that contains an explicit stochastic branching injection, so the central mechanistic conclusion is not yet fully supported.","major_comments":[{"comment":"The soft-spot model contains an explicit stochastic branching source: a competing soft spot is added with probability p_ir = 0.01 whenever the dynamics reaches a system-wide configuration that has not been visited previously, and without this injection the model reaches a limit cycle for any amplitude (Ref. [30]). The paper's central mechanistic claim—that branching originates from competition between nearly-degenerate plastic instabilities—is therefore partly constructed, because the competing instability is injected stochastically rather than emerging from the natural threshold disorder. The manuscript does not report how the waiting-time distribution or the branching rate depend on p_ir, nor does it show in the particle simulations that a small perturbation reverses the ordering of two nearly-degenerate instabilities. To support the mechanism claim, the authors should either vary p_ir and show that the branching statistics are robust as p_ir is reduced (with near-degenerate pairs arising from threshold disorder), or present direct evidence in the particle simulations that a perturbation changes which of two nearly-degenerate instabilities activates first.","section":"Supplementary Material, 'Soft-spot model' paragraph after Eq. (12)"},{"comment":"The branching event is not quantitatively defined. The waiting-time distribution and the branching rate λ_b (Fig. 3a) depend on a criterion for when two trajectories 'separate,' but the paper does not state it—for example, a threshold value of Dr, a stress-signal mismatch, or the first plastic event with a different activation sequence. Without an explicit criterion, the exponential fit in Fig. 2b and the power-law exponent β = 1.34(7) cannot be independently reproduced or checked for robustness against the choice of threshold. A precise definition and a sensitivity analysis should be added.","section":"Results, 'waiting times' paragraph and Fig. 2b; Supplementary Material"},{"comment":"The negative claim that sustained exponential sensitivity to initial conditions is ruled out is stronger than the data support. The experiment uses N = 1000 particles, δ = 10^-9, and about 100 cycles; a finite-time Lyapunov analysis over this horizon, with rare branching events, can rule out large positive exponents but not arbitrarily small ones, and the absence of exponential divergence could be size- or protocol-dependent. The authors should soften the claim or provide a quantitative upper bound on the finite-time Lyapunov exponent consistent with their data.","section":"Results, 'trajectory stability' paragraphs and Fig. 1"}],"minor_comments":[{"comment":"The caption contains a typo: 'becoms' should be 'becomes'.","section":"Fig. 1 caption"},{"comment":"The sentence 'we calculated the slope for the squared distance (Fig. 3a)' appears to reference the wrong panel; the mean-square distance is shown in Fig. 3b.","section":"Main text after Eq. (6)"},{"comment":"The statement 'Once a previously visited system-wide configuration is reached, we set p_ir = 0' is ambiguous: it is unclear whether p_ir is set to zero for the remainder of the simulation after the first return, or only at that specific step. This affects whether branching can occur after a return and should be clarified.","section":"Supplementary Material, 'Soft-spot model' paragraph"},{"comment":"The derivation of the exponential waiting-time distribution assumes that strain intervals between successive plastic events are exponentially distributed. This assumption should be verified explicitly for the present particle simulations, since the cited observations were made in other settings.","section":"Supplementary Material, Eqs. (17)-(26)"},{"comment":"The perturbation magnitude differs between the particle simulations (δ = 10^-9) and the soft-spot model (δ = 10^-5), and no test of the sensitivity of the branching rate to δ is reported. Since branching is threshold-mediated, δ may enter the rate; the authors should state the expected insensitivity or provide a check.","section":"Results, Fig. 3 and perturbation protocols"},{"comment":"The branching diagram uses line thickness to represent the number of perturbed trajectories along a path, but no quantitative key is provided.","section":"Fig. 1(d)"}],"recommendation":"major_revision","confidential_remarks":"The direct particle-simulation result is solid and publishable, but the mechanistic conclusion is currently underpinned by a soft-spot model with an explicit stochastic branching parameter p_ir. Before acceptance, the authors should either demonstrate robustness of the model's statistics to p_ir, provide direct atomistic evidence for the instability-competition mechanism, or reposition the mechanism claim as a model-based prediction rather than an established microscopic origin. The lack of a precise branching-event definition is a reproducibility issue that should also be addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper has a strong negative result and a weaker mechanism section. The particle-based AQS simulations directly probe trajectory stability, and they show that in the post-yield regime perturbations decay rather than grow. That is a clean, important result. It overturns the earlier chaos suggestion, including from one of the same authors, and it is backed by clean exponential waiting-time statistics between branching events. That part of the paper is solid and deserves to be published.\n\nThe soft-spot model bothers me more than your report suggests. The model has an explicit stochastic injection channel: with probability p_ir=0.01, a competing soft spot is added whenever a new system-wide configuration appears. Without that injection, the model always reaches a limit cycle. So the branching statistics in the model are partly by construction. The authors do show a concrete example where two soft spots have nearly equal distances to instability and a tiny perturbation flips the order, which is a plausible mechanism. But that example comes from a model where branching is planted, not from the particle simulations. The particle simulations establish that branching happens; they do not directly show the competition between near-degenerate instabilities. So the claim that instability-selection competition is the generic microscopic mechanism is not as strongly supported as the text suggests. This is fixable: they could test how the branching rate depends on p_ir, and ideally look for the competition signature in the particle simulations.\n\nOther concerns are minor: no code or data released (matters for a negative claim about chaos), only one system size (N=1000), and the branching event detection threshold is not quantitatively specified in the main text. None of these break the central claim.\n\nOverall, the paper is worth a serious referee. The no-chaos result is important and will be cited regardless of the mechanism. The mechanism part needs revision or softening, and the authors should address the p_ir issue directly. I would accept it conditionally.","headline":"The no-chaos result from particle simulations is a real contribution; the mechanism story leans too hard on a model with planted branching.","tokens_in":14466,"tokens_out":3615,"would_cite":true,"duration_ms":30546,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Cyclically sheared amorphous solids do not become irreversible through chaos; they remain locally stable and split through rare branching events caused by competition between nearly degenerate plastic instabilities.","keywords":["amorphous solids","irreversibility transition","athermal quasistatic shear","yielding","trajectory branching","local stability","plastic instabilities","soft-spot model"],"falsifier":"Run the soft-spot model with the probability of adding a competing instability set to zero and remeasure the post-yield branching rate; if branching disappears, the planted randomness rather than natural threshold disorder is the source of the branching statistics, and the microscopic competition mechanism would not be established.","tokens_in":13404,"feed_emoji":"🔄","tokens_out":14471,"duration_ms":110999,"temperature":0.7,"pith_summary":"This paper asks how a deterministic, dissipative material can lose memory of its starting state under repeated shear. In particle simulations, small perturbations to the coordinates decay exponentially even when the shearing amplitude is large enough that the material never settles into a repeating pattern, so the dynamics is locally stable and chaotic divergence is ruled out. Instead, trajectories stay close for a random time and then separate in sudden branching events, after which they diffuse apart. Tracking soft spots—localized zones that rearrange—in a mean-field model shows the trigger: a tiny perturbation decides which of two almost equally unstable regions yields first, scrambling the sequence of all later rearrangements. The paper proposes this instability-selection branching as the generic dynamical route to irreversibility in cyclically driven disordered systems.","feed_headline":"Why sheared glasses lose memory: branching, not chaos","feed_subtitle":"Even above yielding, nearby paths stay stable; rare competitions between nearly tied plastic events split them","key_machinery":"The ordering of plastic events is controlled by the distance to instability $x_i$, the gap between each soft spot's current stress and its activation threshold; the next event is the soft spot with the smallest (most negative inside an avalanche) $x_i$. Branching occurs when two sites form a nearly-degenerate pair, quantified by the competition variable $\\Delta = x_{187} - x_{157}$ in the example: a perturbation of order $10^{-5}$ flips the sign of $\\Delta$, changing which instability activates first. The mean-field soft-spot model with hysteretic elements gives direct access to soft-spot identities and activation order, allowing the paper to watch the competition event by event, while the derivation of the exponential waiting-time distribution uses the known exponential distribution of strain intervals between plastic events under AQS loading.","core_discovery":"The central discovery is that irreversibility in the post-yield regime of cyclically sheared amorphous solids is produced by persistent trajectory branching, not by exponential sensitivity to initial conditions. Under athermal quasistatic shear, a small perturbation of a trajectory decays rapidly even when the system never returns to a periodic limit cycle; the trajectory is locally stable in the sense of contracting perturbations. Separation happens only when a plastic event selects between two nearly-degenerate instabilities: each unstable soft spot has a distance to instability $x_i=\\sigma_i^+ - \\sigma_i$, and when two sites are almost tied for the smallest $x_i$, a perturbation of order $10^{-9}$ in the particle model or $10^{-5}$ in the soft-spot model flips which one activates first. The losing instability is not erased but acts later, so the entire sequence of plastic events is reordered and the trajectories land on different branches. After branching the trajectories decorrelate and separate diffusively, with the squared separation growing with slope $8D$ in two dimensions, twice the self-diffusion coefficient. Waiting times between branchings are exponentially distributed, which the paper derives from a constant per-event branching probability, and the branching rate grows as a power law of strain amplitude above yield.","pith_inferences":["If near-degeneracy is the real trigger, widening the disorder in instability thresholds should suppress branching at fixed strain amplitude; this is a direct prediction the paper does not test.","The soft-spot model adds a competing instability with probability $p_{ir}=0.01$ only when a new configuration appears; varying this probability as a control parameter would separate the contribution of planted randomness from that of the natural threshold disorder, a distinction the current simulations do not resolve.","Because the mechanism reorders activation sequences, it may unify the irreversibility transition with multi-periodic memory and cascade-scrambling phenomena in the same systems; the paper notes the relation but leaves the common statistical description for future work.","A direct experimental test in colloidal or granular cyclically sheared systems would be to track pairs of nearby tracer particles: the paper's picture predicts plateaus of near-constant separation punctuated by sudden jumps, rather than smooth exponential growth."],"forward_implications":["Above yielding, a positive Lyapunov exponent is not required for irreversibility; local stability can coexist with persistent trajectory separation.","The branching rate factorizes as $\\lambda_b = p_b \\lambda_{pl}$, so the irreversibility transition can be described by a constant per-plastic-event probability of branching once the plastic-event rate is known.","Post-branching separation grows diffusively with slope $S = 8D$ in two dimensions, meaning branched trajectories are statistically independent and the separation directly measures the material's self-diffusion.","The branching rate increases as $\\lambda_b \\sim (\\gamma_{\\max} - \\gamma_c)^\\beta$ with $\\beta = 1.34(7)$, connecting the dynamical mechanism to the critical behavior of the irreversibility transition.","The same exponential waiting-time statistics appear in both a particle-based model and a mean-field soft-spot model, suggesting the mechanism is generic across driven disordered systems such as colloids, granular materials, and emulsions."],"supporting_citations":[{"why":"Defines the soft-spot model of overlapping plastic events that the paper uses to identify the microscopic branching mechanism.","marker":"[30]"},{"why":"Provides the binary Lennard-Jones particle model used for the athermal quasistatic shear simulations.","marker":"[36]"},{"why":"Proposed chaos and positive Lyapunov exponents in sheared suspensions, the hypothesis the paper directly tests and rules out for amorphous solids.","marker":"[12]"},{"why":"Earlier time-series analysis suggested chaotic dynamics in amorphous solids under periodic shear and is the claim being revisited.","marker":"[1]"},{"why":"Documents the approximately exponential distribution of strain intervals between plastic events under AQS loading that the waiting-time derivation uses.","marker":"[37]"},{"why":"Provides avalanche and threshold statistics for mesoscale amorphous plasticity used in the same derivation.","marker":"[43]"},{"why":"Reports critical diffusivity above the yielding transition, with which the measured branching-rate power law is compared.","marker":"[42]"},{"why":"Identifies cascade-scrambling of activation order in cyclically sheared amorphous solids, the mechanism the paper links to its branching scenario.","marker":"[47]"},{"why":"Gives the dynamical-systems definitions of local stability and chaotic divergence used to interpret perturbation decay.","marker":"[38]"}],"fun_headline_variants":["Sheared glasses branch, not chaos, to lose memory","Memory loss in sheared glasses from rare branching events","Irreversibility in amorphous solids: branching wins over chaos","Cyclically sheared glasses: no chaos, just branchings","Soft spots split, paths diverge: how glasses forget"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the soft-spot model's rule—injecting a competing instability with probability 0.01 whenever a new configuration appears—faithfully represents how real amorphous solids resolve nearly simultaneous plastic events; if that injected randomness is what creates the branching statistics, the claimed microscopic mechanism would be weakened.","fun_headline_variants_meta":{"raw":{"variants":["Sheared glasses branch, not chaos, to lose memory","Memory loss in sheared glasses from rare branching events","Irreversibility in amorphous solids: branching wins over chaos","Cyclically sheared glasses: no chaos, just branchings","Soft spots split, paths diverge: how glasses forget"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000197,"raw_usage":{"total_tokens":1369,"prompt_tokens":953,"completion_tokens":416,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":569,"completion_tokens_details":{"reasoning_tokens":333}},"tokens_in":569,"tokens_out":416,"duration_ms":4847,"temperature":1.0,"reasoning_tokens":333,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T10:48:45.275286+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the soft-spot model with the probability of adding a competing instability set to zero and remeasure the post-yield branching rate; if branching disappears, the planted randomness rather than natural threshold disorder is the source of the branching statistics, and the microscopic competition mechanism would not be established.","supporting_citations":[{"cited_title":"Overlapping plastic events as a mechanism for irreversible dynamics in amorphous solids under oscillatory shear.Physical Review Research, 6(3):033129, 2024","cited_arxiv_id":null,"evidence_quote":"Defines the soft-spot model of overlapping plastic events that the paper uses to identify the microscopic branching mechanism."},{"cited_title":"Glass transitions in one-, two-, three-, and four-dimensional binary lennard-jones systems.Journal of Physics: Condensed Matter, 21(3):035117, 2009","cited_arxiv_id":null,"evidence_quote":"Provides the binary Lennard-Jones particle model used for the athermal quasistatic shear simulations."},{"cited_title":"Chaos and threshold for irreversibility in sheared sus- pensions.Nature, 438(7070):997–1000, 2005","cited_arxiv_id":null,"evidence_quote":"Proposed chaos and positive Lyapunov exponents in sheared suspensions, the hypothesis the paper directly tests and rules out for amorphous solids."},{"cited_title":"Maloney and A","cited_arxiv_id":null,"evidence_quote":"Documents the approximately exponential distribution of strain intervals between plastic events under AQS loading that the waiting-time derivation uses."},{"cited_title":"Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity.Physical Review E, 100(4):043003, 2019","cited_arxiv_id":null,"evidence_quote":"Provides avalanche and threshold statistics for mesoscale amorphous plasticity used in the same derivation."},{"cited_title":"Critical diffusivity in the reversibility–irreversibility transition of amorphous solids under oscillatory shear.Journal of Physics: Condensed Matter, 31(4):045101, 2019","cited_arxiv_id":null,"evidence_quote":"Reports critical diffusivity above the yielding transition, with which the measured branching-rate power law is compared."},{"cited_title":"Coopera- tive effects driving the multi-periodic dynamics of cycli- cally sheared amorphous solids.The Journal of Chemical Physics, 156(16):164506, 2022","cited_arxiv_id":null,"evidence_quote":"Identifies cascade-scrambling of activation order in cyclically sheared amorphous solids, the mechanism the paper links to its branching scenario."},{"cited_title":"Ott.Chaos in dynamical systems","cited_arxiv_id":null,"evidence_quote":"Gives the dynamical-systems definitions of local stability and chaotic divergence used to interpret perturbation decay."}],"review_version":1}