{"id":"26beb176-dd98-43d4-a31b-6229a96a4698","arxiv_id":"2511.14872","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Static maximum-entropy thermodynamics cannot distinguish avalanche-critical from supercritical neuronal cultures, though it can separate subcritical from critical/supercritical activity.","lead":"Maximum-entropy models of neurons show 'critical' thermodynamic peaks both for avalanche-critical and for hyper-excitable 'supercritical' cultures, so static ME signatures cannot tell these states apart. The authors confirm this in a tunable integrate-and-fire model and show that only clearly subcritical cultures lack the peaks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract's 'equally strong' claim is contradicted by the paper's own Cv scaling exponents (1.41 vs 1.70, ~3.4σ), so the asserted indiscriminability of critical vs supercritical is quantitatively unsubstantiated.","rationale":"The reader's weakest_assumption focuses on inherited avalanche labels, which is a legitimate concern, but the IF model provides an independent confirmation that does not rely on those labels, so mislabeling would not overturn the qualitative result. I find a more load-bearing issue in the quantitative claim of 'equally strong' thermodynamic signatures. The paper's own data show a significant difference in the finite-size scaling exponent for the specific heat maximum between critical (a=1.41±0.06) and supercritical (a=1.70±0.06) IF networks. This difference (~3.4σ) means the abstract's 'equally strong' is false, and more importantly, it opens a potential discriminator: if the supercritical peak grows faster with system size, then in principle one could use scaling of max[Cv] to tell critical from supercritical. The experimental comparison lacks any formal test, so the claim that static ME thermodynamics cannot discriminate is not quantitatively established. The qualitative separation of subcritical from critical/supercritical is well-supported, so the verdict remains CONDITIONAL, but the specific condition should include a rigorous statistical comparison of the thermodynamic response functions and their scaling between critical and supercritical states. I partially agree with the reader's label concern, but I think the scaling discrepancy is more directly load-bearing for the central conclusion.","tokens_in":19581,"tokens_out":7520,"duration_ms":79472,"concrete_test":"Using the 5 independent IF network realizations per state, compute max[Cv] for N=20,40,80,100 and test whether the critical vs supercritical scaling exponents differ via a permutation test or ANCOVA on log(max[Cv]) vs log N. Also run a Welch's t-test on max[Cv] between the 5 critical and 5 supercritical experimental cultures at N=60. If either test yields p<0.05, the 'equally strong' claim and the indiscriminability conclusion are falsified quantitatively; if not, the paper's claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central negative claim requires that static ME thermodynamics produce equivalent signatures in critical and supercritical states. The paper's own fits in Sec. III.D show max[Cv] ∝ N^a with a=1.41±0.06 for critical IF networks and a=1.70±0.06 for supercritical IF networks (Fig. 5b,c). These exponents differ with high significance (~3.4σ), contradicting the abstract's 'equally strong.' No statistical test is reported for the experimental comparison (5 vs 5 cultures, N=60), so the comparable-strength assertion is purely qualitative there as well. If supercritical max[Cv] grows faster with N, a finite-size scaling analysis could in principle distinguish critical from supercritical, meaning the paper has not established that static ME models cannot discriminate. The qualitative point—that subcritical models lack pronounced peaks while critical and supercritical both show them—is convincing, but the stronger indiscriminability claim is not.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates whether static maximum-entropy (ME) models of neuronal populations can distinguish avalanche criticality from subcritical and supercritical dynamics. Using K-pairwise ME models (fields, pairwise couplings, and a synchrony potential) inferred from organotypic cortex slice cultures classified by avalanche metrics, and from a tunable integrate-and-fire (IF) network model, the authors compute specific heat and susceptibility as functions of a temperature-like parameter. They report pronounced maxima near T=1 for critical and supercritical systems, but not for subcritical systems, and conclude that ME thermodynamics separates subcritical from critical/supercritical states but cannot discriminate between criticality and supercriticality. The IF model provides independent support, and an unconstrained three-point correlation check is included.","tokens_in":19869,"tokens_out":6352,"duration_ms":62801,"significance":"If correct, the result is significant: it challenges the use of static ME thermodynamic signatures as a unique marker of avalanche criticality and underscores the need for dynamical measures. The paper's strengths include a tunable IF model that reproduces the experimental observations, explicit discussion of prior work on inference-induced criticality, and a validation against unconstrained three-point correlations. However, the quantitative support for the stronger claim of 'equally strong' signatures is incomplete, and the experimental sample description is ambiguous. The qualitative distinction between subcritical and critical/supercritical systems is convincing, but the stronger indiscriminability claim requires additional statistical support.","major_comments":[{"comment":"The abstract and conclusions state that critical and supercritical models show 'equally strong' thermodynamic signatures, but the paper's own finite-size scaling for the specific heat gives max[Cv] ∝ N^a with a=1.41±0.06 (critical) and a=1.70±0.06 (supercritical). The difference is ~3.4 standard errors, so the growth rates are significantly different. Thus, at least for the IF model, a finite-size scaling analysis can distinguish critical from supercritical, directly contradicting the indiscriminability claim. For the experimental data (5 per condition, N=60), no statistical test is reported for the comparison; error bars alone do not establish 'equally strong.' The qualitative claim about subcritical vs critical/supercritical is convincing, but the stronger claim needs to be reformulated or supported by a formal equivalence test (e.g., confidence intervals on the ratio of maxima, or a B","section":"Sec. III.D and Fig. 5"},{"comment":"The text states that 15 recordings were analyzed, 5 for each condition, and Fig. 1 indicates different neuronal cultures. However, the Fig. 6 caption says the shaded areas are 'the standard error obtained from 5 experimental subsamples of the same cortical culture.' These statements are inconsistent. If the five datasets per condition are subsamples of a single culture, then the effective sample size is one per condition, and the error bars do not reflect across-culture variability; the conclusions about 'cultures' are then not generalizable. The authors must clarify the experimental design and, if the data are indeed from five different cultures, correct the caption.","section":"Sec. II.B and Fig. 6 caption"},{"comment":"The analysis inherits the critical/subcritical/supercritical classification from Shew et al. [28] without re-deriving or validating it for these recordings. One of the five 'subcritical' cultures (AP5-only) behaves thermodynamically like the critical cultures, and the authors treat this as an exception, arguing that only combined AP5/DNQX treatment truly drives cultures subcritical. This is a post hoc reinterpretation of the label. If the avalanche-based label is the ground truth, then this culture is a counterexample to the claim that ME thermodynamics 'correctly distinguishes' subcritical systems; if the label is not reliable, then the three-way comparison itself is called into question. Please provide a sensitivity analysis excluding the AP5-only culture, or an independent validation of the labels (e.g., re-computing avalanche exponents for all 15 recordings).","section":"Sec. III.B and Fig. S12"}],"minor_comments":[{"comment":"No code or data availability statement is provided. The Boltzmann Machine learning procedure and Monte Carlo sampling are central to the results; releasing code/data would substantially aid reproducibility.","section":"General"},{"comment":"The threshold for fitting VK (P(K)>1e-4 for experimental data, >1e-5 for numerical data) is described as heuristic. Please report the sensitivity of the thermodynamic quantities (Cv, χ) and the inferred VK to this threshold.","section":"Sec. III.A"},{"comment":"The spin-glass-like low-temperature region (T<T*) is identified by initial-configuration dependence. Please clarify how T* is determined, and whether the reported maxima near T=1 are affected by the finite sampling at temperatures close to T*.","section":"Sec. III.D"},{"comment":"Typographical and notation issues: 'In constrast' (p.10), inconsistent use of 'Vk' vs 'VK', and Tijk is sometimes written without subscript formatting. The allometric scaling subsection (II.C.1) appears tangential to the main argument and could be shortened or moved to the SI.","section":"Miscellaneous"},{"comment":"Reference [40] is a preprint; please update if it has been published in the interim.","section":"References"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something genuinely useful: it tests whether the thermodynamic signatures of inferred maximum-entropy models track avalanche-based criticality labels. On organotypic cultures and a tunable IF network, the authors show that subcritical systems are distinguishable—weak or absent Cv/chi peaks—while critical and supercritical systems both show pronounced peaks near T=1. That qualitative result is convincing, and the IF-network confirmation is a real independent check, even though the model is the authors' own. The unconstrained three-point-correlation check is good practice. Prior theory predicted that inferred ME models can look critical regardless of dynamics; this paper supplies the direct empirical demonstration.\n\nThe soft spots are real, though. The abstract's 'equally strong' is contradicted by their own numbers: for the IF model, max[Cv] scales as N^1.41 for critical and N^1.70 for supercritical, a difference of about 3.4 sigma. So the supercritical peak actually grows faster with system size. That weakens the claim that ME thermodynamics cannot discriminate; with a proper finite-size scaling analysis, they might be separable after all. The experimental comparison (5 vs 5 cultures) has no formal statistical test, so 'equally strong' is purely qualitative there. The avalanche labels are inherited from Shew et al. 2009 and treated as ground truth; the one AP5-only culture that thermodynamically behaves like critical is set aside as an exception. That handling is reasonable, but the label uncertainty should be flagged rather than buried. No code or data is shipped, so the experimental half is not independently reproducible.\n\nI would not call the Hamiltonian-fitting circular—the paper frames its result as comparative, and the peaks are properties of the fitted model, which is the standard usage. The self-citations to the authors' own IF model are fine because the model is described in the paper.\n\nBottom line: this is a worthwhile caveat for anyone using ME thermodynamic peaks as a criticality biomarker. It deserves peer review, but the strong indiscriminability claim should be softened or backed by a formal comparison of peak heights and scaling exponents. Send it to referees.","headline":"The qualitative point is solid and useful, but the central 'equally strong' claim is undercut by the paper's own scaling exponents.","tokens_in":20362,"tokens_out":2720,"would_cite":true,"duration_ms":26247,"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":"Static maximum-entropy models of neural populations show equally strong thermodynamic criticality signatures for critical and supercritical cortical cultures, so static thermodynamics alone cannot certify avalanche criticality.","keywords":["maximum entropy models","neuronal avalanches","criticality","specific heat","K-pairwise Ising model","synchrony distribution","cortical slice cultures","integrate-and-fire network"],"falsifier":"A decisive test: in the tunable integrate-and-fire network, set the recovery parameter to a supercritical value while holding firing rates and pairwise correlations at subcritical levels; if the inferred K-pairwise model still shows a specific-heat maximum near T = 1, the thermodynamic signature is not merely an artifact of firing-rate levels, whereas if the peak vanishes, the paper's main conclusion fails to generalize beyond correlated-activity level. Independently, an avalanche-classified supercritical culture whose inferred model shows no peak near T = 1 would directly refute the claim.","tokens_in":19487,"feed_emoji":"🧠","tokens_out":8974,"duration_ms":82107,"temperature":0.7,"pith_summary":"This paper asks whether the thermodynamic signatures of criticality seen in maximum-entropy (ME) models of neural populations track dynamical criticality as defined by neuronal avalanches. Using organotypic rat cortex cultures in baseline, hypo-excitable, and disinhibited states, plus an integrate-and-fire network model that can be tuned to and away from criticality, the authors infer K-pairwise Ising-like models from every condition. They find that models inferred from critical and supercritical cultures both show pronounced specific-heat and susceptibility peaks near the model's unit temperature, with the peaks growing superlinearly with system size, whereas models from subcritical cultures show no such peaks. The paper concludes that static ME thermodynamics separates subcritical systems from critical/supercritical ones but cannot discriminate avalanche criticality from supercriticality; dynamical information is needed for that distinction.","feed_headline":"Static brain models misread supercritical activity as critical","feed_subtitle":"Specific-heat peaks near the model's unit temperature appear for critical and over-excited cultures alike; only avalanches separate them.","key_machinery":"The carrying object is the K-pairwise Ising-like model, a maximum-entropy distribution of the form P(σ) ∝ exp[Σ_i h_i σ_i + ½Σ_{i≠j} J_ij σ_i σ_j + Σ_K V_K δ_{K,K'(σ)}], where σ_i is the binary spiking state of neuron or electrode i, h_i are local fields setting firing rates, J_ij are pairwise couplings fixing correlations, and the potentials V_K constrain the probability that exactly K units fire together. Parameters are learned from data by iterative gradient descent that matches model averages to data averages; a temperature T rescales all parameters, and at T = 1 the model reproduces the measured statistics. The argument is carried by the temperature dependence of the specific heat C_v a","core_discovery":"Central discovery: a mismatch between static and dynamic criticality signatures. ME models fitted to time-averaged firing rates, pairwise correlations, and synchrony distribution reproduce avalanche classifications only partially: subcritical systems give flat, weak specific heat and susceptibility, while critical and supercritical systems both give strong maxima near T = 1 that grow faster than linearly with population size. Because supercritical cultures were independently classified by avalanche statistics and showed poor dynamic range, the thermodynamic peak cannot be evidence of dynamical criticality. The same pattern appears in an integrate-and-fire network tuned below, at, and above c","pith_inferences":["The thermodynamic peak is likely a generic property of strongly correlated binary models with sufficiently high firing rates and correlations, not a marker of critical dynamics; if so, reports of ME 'criticality' in other neural datasets may need re-examination unless they also check avalanche scaling.","The one AP5-treated culture labeled subcritical but thermodynamically critical suggests that the subcritical label depends on which excitatory receptors are blocked; a graded pharmacology experiment varying NMDA versus AMPA receptor blockade could trace where the thermodynamic signature disappears.","The V_K large-K signal could be turned into an explicit static discriminator (for instance, a threshold on V_K for K/N > 0.75) and validated against avalanche classification on an independent set of cultures.","Because the integrate-and-fire model reproduces the effect while allowing full control of the tuning parameter, it offers a direct platform to test whether any static statistic can separate critical from supercritical states, or whether that separation is information-theoretically impossible from time-averaged data."],"forward_implications":["Static ME thermodynamics is not a standalone biomarker for brain criticality: a pronounced specific-heat peak near T = 1 can arise from supercritical, functionally degraded cultures just as from critical ones.","The subcritical versus critical/supercritical divide is thermodynamically visible, so ME models remain useful for detecting strong reductions in excitability.","Among the fitted parameters, the high-synchrony potentials V_K at large K separate supercritical from critical states in most datasets, suggesting a static observable that may partly encode the dynamical regime.","Adding the synchrony distribution P(K) as a constraint improves the models' prediction of unconstrained three-point correlations, strengthening the case for K-pairwise over purely pairwise ME models.","Distinguishing true criticality from supercriticality requires dynamic signatures, such as avalanche size and duration scaling or ME constraints that include temporal information."],"fun_headline_variants":["Static brain models misread over-excited activity as critical","Thermodynamic criticality peak fools static neural models","Static entropy models cannot separate critical from supercritical","Criticality signal emerges in supercritical cortex models too","Model specific heat peaks mislead about neural criticality"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The results assume that the three-way division of the 15 recordings into critical, subcritical, and supercritical states, taken from a previous avalanche-based study, is correct; if some cultures are mislabeled—as the single AP5-treated culture suggests—then the claim that static ME models cannot distinguish critical from supercritical is only established for that particular labeling.","fun_headline_variants_meta":{"raw":{"variants":["Static brain models misread over-excited activity as critical","Thermodynamic criticality peak fools static neural models","Static entropy models cannot separate critical from supercritical","Criticality signal emerges in supercritical cortex models too","Model specific heat peaks mislead about neural criticality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001449,"raw_usage":{"total_tokens":5695,"prompt_tokens":788,"completion_tokens":4907,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":532,"completion_tokens_details":{"reasoning_tokens":4831}},"tokens_in":532,"tokens_out":4907,"duration_ms":30795,"temperature":1.0,"reasoning_tokens":4831,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:33:50.570478+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test: in the tunable integrate-and-fire network, set the recovery parameter to a supercritical value while holding firing rates and pairwise correlations at subcritical levels; if the inferred K-pairwise model still shows a specific-heat maximum near T = 1, the thermodynamic signature is not merely an artifact of firing-rate levels, whereas if the peak vanishes, the paper's main conclusion fails to generalize beyond correlated-activity level. Independently, an avalanche-classified supercritical culture whose inferred model shows no peak near T = 1 would directly refute the claim.","supporting_citations":[],"review_version":1}