{"id":"f05d6490-0c88-44e1-a45b-57304b6f34f6","arxiv_id":"2412.19182","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors reaffirm their no-go theorem for psi-ontic models, arguing that Gao's criticism misreads the Harrigan-Spekkens framework's classical treatment of statistical mixtures.","lead":"This short paper answers a critic who argued that the authors' earlier no-go theorem against psi-ontic quantum models relies on a hidden classical assumption. The authors reply that the assumption is already part of the Harrigan-Spekkens framework they are criticizing, so the theorem stands.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The no-go conclusion does not follow from the HS mixing assumption unless Shannon/Gibbs entropy is shown to be the only available entropy; the response leaves alternatives open, so it proves a conditional inconsistency rather than a theorem against all psi-ontic HS models.","rationale":"The reader's weakest assumption concerns the premise that HS already assumes classical mixing and hence Shannon entropy. I agree that this premise is the contested hinge, but I would sharpen it: even granting full classical convex mixing, the paper does not bridge from that premise to the mandatory use of Shannon/Gibbs entropy. The response's own schematic argument (Section 2) presents the move as an entitlement ('we should be entitled to use the only tools we have'), not as a proven implication; and Section 3 explicitly leaves open the possibility of a different entropy definition. That admission is in tension with the paper's concluding claim that the no-go theorem is 'true' and that Gao's criticism is rejected. The no-go theorem can be correct only if it rules out all possible entropy functionals on the ontic-state space, not just the Shannon/Gibbs one. The response does not supply such an impossibility proof, so its defense of the theorem remains conditional on a substantive choice that Gao is entitled to question. This does not require moving the reader's verdict: CONDITIONAL already captures 'plausible but not settled.' My concern is more specific about where the gap lies; hence partial agreement.","tokens_in":6615,"tokens_out":6946,"duration_ms":73057,"concrete_test":"First locate in Carcassi et al. (2024) the exact operational quantity whose quantum-mechanical value is the von Neumann entropy and which a successful ontological model must reproduce. Then, with that quantity fixed, re-derive Step 4 of the Section 2 argument using an alternative entropy functional on M(Lambda)—for example Renyi-2 entropy, or an entropy generated by a metric on Lambda that makes the supports of two non-orthogonal states overlap. If the alternative functional reproduces the required von Neumann value for all HS convex mixtures, the no-go theorem fails; if no such functional exists, the no-go claim is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Premise 1 of the schematic argument in Section 2—that HS models represent mixed preparations by convex combinations of epistemic states, i.e. by Kolmogorov probability measures—may be granted; it is indeed part of Harrigan and Spekkens' framework. The load-bearing step is the next one: 'Given that mixtures ... are modeled as classical probability distributions, we should be entitled to use the only tools we have that work on those (i.e. classical statistical mechanics).' This is not a mathematical implication. A probability measure admits many entropy functionals (Renyi, metric-based, or an explicitly constructed map to density matrices), and the response itself concedes in Section 3 that 'one may give a different definition of entropy to use on the ontic space' and that the authors are 'open to the possibility that there may be something that can be made to work.' A no-go theorem for all psi-ontic HS models requires ruling out every such alternative, not merely showing that the Shannon/Gibbs functional fails to reproduce the von Neumann entropy. The paper's conclusion therefore overstates what its premises establish: the argument demonstrates a conflict between the HS convex-mixing rule plus Shannon entropy and quantum thermodynamics, not the impossibility of psi-ontic models under the HS definitions. This also reconnects to Gao's original complaint: the Shannon entropy encodes a particular kind of distinguishability, and the response does not show why the HS framework is committed to that encoding merely by using convex combinations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This note responds to Shan Gao's criticism of the authors' earlier no-go theorem for ψ-ontic models in the Harrigan-Spekkens (HS) framework. The authors argue that the allegedly implicit assumption of classical mixing of epistemic states is in fact already part of the HS framework, so the use of Shannon/Gibbs entropy is justified. They further claim that Gao neither addresses the outstanding problems of recovering quantum statistical mechanics, thermodynamics, and information theory from an ontological model, nor explains how to compute a von Neumann entropy from an epistemic state. The paper concludes that Gao's criticism is rejected, reiterates that the no-go theorem is correct, and draws broader consequences for the interpretation of the PBR theorem.","tokens_in":6829,"tokens_out":4023,"duration_ms":40316,"significance":"If fully established, the no-go theorem would be a significant result in quantum foundations: it would show that ψ-ontic models as defined by Harrigan and Spekkens cannot reproduce quantum mechanics, thereby undermining a widely used classification scheme and altering the standard reading of the PBR theorem. The present response does clarify the structure of the authors' argument and honestly lists several open problems, which is a strength. However, the central logical gap identified by Gao and by the stress-test review remains: the step from the HS mixing rule to the unique applicability of Shannon/Gibbs entropy is not proved. The paper's conclusion therefore overstates what its premises establish, and the response functions more as a clarification of the authors' position than as a definitive refutation of the criticism.","major_comments":[{"comment":"The inference from 'mixtures in the HS model are modeled as classical probability distributions' to 'we should be entitled to use the only tools we have that work on those (i.e. classical statistical mechanics)' is not a mathematical consequence. A Kolmogorov probability measure on the ontic space admits many entropy functionals, such as Rényi entropies or other measures satisfying different axioms. The paper itself concedes in Section 3 that 'one may give a different definition of entropy to use on the ontic space' and that 'we are open to the possibility that there may be something that can be made to work.' This concession directly undermines the no-go conclusion: the argument at most demonstrates a conflict between the HS convex-mixing rule plus Shannon/Gibbs entropy and quantum thermodynamics, not the impossibility of all ψ-ontic HS models. To sustain the theorem, the authors must either prove that the HS definitions force the Shannon/Gibbs entropy, or rule out all alternative entropy functionals, neither of which appears in this response.","section":"Section 2, premise 4"},{"comment":"The central defense—that the classical-mixing assumption is 'an assumption made by Harrigan and Spekkens'—rests on a reading of HS that is exactly what Gao contests. The quotes from Gao and HS establish that the HS framework represents mixtures by weighted sums of probability measures, but they do not show that this entails Shannon/Gibbs entropy as the entropy functional for epistemic states. The paper relies on the authors' prior article (Carcassi et al. 2024) for this interpretation, yet that article is precisely the subject of the dispute, so the argument is circular. To reject Gao's criticism, the response must provide an independent derivation from the HS definitions that the Shannon/Gibbs entropy is the unique or forced choice, or explicitly acknowledge that the no-go theorem is conditional on this choice.","section":"Section 2, §2 response to Gao"}],"minor_comments":[{"comment":"The response is not self-contained: the no-go theorem is not stated in this note, and the reader is referred to Carcassi et al. (2024). Stating the theorem and a brief proof sketch would make the paper more accessible and avoid ambiguity about the exact claims being defended.","section":"General"},{"comment":"The phrase 'raised by Carcassi in a signed response as part of the peer-review process' refers to an unpublished process and is not verifiable; it should be removed or replaced with a citation to a publicly available document.","section":"Section 3"},{"comment":"The discussion of Bohmian mechanics, while relevant to the scope of the no-go theorem, is only loosely connected to the direct response to Gao and could be condensed or moved to a separate paper to keep the reply focused.","section":"Section 4"},{"comment":"Occasional rhetorical overstatement, such as 'the theorem proved in our paper is correct, and therefore true' and 'the HS model framework is fundamentally flawed,' conflicts with the paper's own acknowledgment that alternative entropy definitions might work; more careful phrasing would better match the actual strength of the argument.","section":"Various"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reply to a criticism and does not present new technical results. The main concern is the unproved uniqueness of the Shannon/Gibbs entropy under the HS framework. The authors' admission that alternative entropy functionals 'may be made to work' effectively concedes the stress-test objection. A major revision should either prove that HS forces the Shannon/Gibbs entropy or reframe the result as conditional, and should also address the circularity of relying on the disputed prior paper. The paper's philosophical discussion of PBR is interesting but secondary. Given the journal's scope, a response is appropriate, but the logical gap is load-bearing."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a reply, not a new theorem. It restates the earlier no-go argument, adds a critique of Gao for ignoring quantum statistical mechanics, and draws philosophical conclusions about PBR. What it does well: it is clearly written, honest about what it assumes, and it correctly notes that HS mixtures are convex combinations of probability measures. Gao's \"implicit assumption\" charge is partly unfair—the classical mixing is in HS, not smuggled in by the authors. The response also makes a fair point that Gao never engages with the need to reproduce quantum statistical mechanics, not just the entropy.\n\nThe soft spot is the load-bearing step. From \"mixtures are probability measures\" it does not follow that Shannon/Gibbs is the only entropy available, nor that one is entitled to use it because classical statistical mechanics is the only tool. The paper itself concedes in Section 3 that \"one may give a different definition of entropy to use on the ontic space\" and says the authors are open to this. A no-go theorem against all psi-ontic HS models requires ruling out those alternatives. As written, the result is a conditional inconsistency: HS convex mixing plus Shannon entropy cannot reproduce the von Neumann entropy. That is not the same as showing psi-ontic models in HS are impossible. The stress-test note is right about this.\n\nThere is also a smaller issue with the claim that Kolmogorov probability \"already assumes that all elements are equally distinguishable.\" That depends on the sigma-algebra separating points. If HS allows coarse-grained measurable structure, the argument needs more work. The reply does not address that.\n\nBottom line: the paper is a serviceable contribution to an ongoing dispute, and the authors are right that Gao understated their context. But the universal no-go conclusion overreaches what this response proves. It deserves peer review as a reply, but I would not cite it as a standalone result—cite the original and treat this as a clarification. Reading group: maybe, if you are following the HS debate.","headline":"A clear, honest reply that correctly pins the classical-mixing premise on HS, but it does not close the gap Gao pointed to: the argument shows Shannon entropy fails, not that no entropy on ontic states can work.","tokens_in":7394,"tokens_out":2174,"would_cite":false,"duration_ms":24362,"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":"The paper defends its no-go theorem against Gao's criticism: Harrigan-Spekkens psi-ontic models already assume classical probability mixtures, so the entropy mismatch is a theorem, not an extra premise.","keywords":["psi-ontic models","Harrigan-Spekkens framework","ontological models","Shannon entropy","von Neumann entropy","PBR theorem","quantum statistical mechanics","no-go theorem"],"falsifier":"Render the theorem false by constructing an explicit Harrigan-Spekkens psi-ontic model whose epistemic states are classical probability measures over ontic states and that still reproduces the von Neumann entropy of, say, an equal mixture of spin-up along z and spin-up along x (or that derives the Holevo bound). Producing such a model with its density-matrix outcome probabilities would directly contradict the no-go claim.","tokens_in":6358,"feed_emoji":"⚛️","tokens_out":5925,"duration_ms":55053,"temperature":0.7,"pith_summary":"This note responds to a published criticism of the authors' earlier no-go theorem for psi-ontic models. It argues the criticism misses the structure of the theorem: the Harrigan-Spekkens framework itself represents quantum statistical mixtures as classical probability distributions over ontic states, so the Shannon/Gibbs entropy is the only entropy available to the model. Since the Shannon entropy of a quantum mixture does not equal its von Neumann entropy, a psi-ontic model in this framework cannot reproduce quantum statistical mechanics. The paper concludes that the theorem stands, that the Harrigan-Spekkens categorization is flawed, and that the PBR theorem should not be read as establishing the reality of the quantum state.","feed_headline":"No-go theorem for psi-ontic models survives criticism","feed_subtitle":"A reply locates the 'too classical' premise inside the Harrigan-Spekkens model itself, not in the entropy argument.","key_machinery":"The central object is the epistemic state of the Harrigan-Spekkens framework: a probability measure $p(\\lambda|P)$ over the ontic state space $\\Lambda$, with a mixture of pure states represented as $\\sum_i p_i\\, p(\\lambda|P_{\\psi_i})$. The argument's engine is the entropy conflict: because this is a Kolmogorovian probability measure, the Shannon/Gibbs entropy is the natural and only thermodynamic entropy on the space of such measures, but the quantum mixture it represents requires the von Neumann entropy, which cannot be computed from a classical measure. The $\\sigma$-algebra structure of a Kolmogorov space is what makes all ontic states distinguishable in principle.","core_discovery":"Gao's objection was that the entropy argument implicitly assumes non-orthogonal ontic states are classically distinguishable. The authors reply that no extra assumption was made: a classical probability measure over ontic states automatically distinguishes every element of its sigma-algebra, and the Harrigan-Spekkens framework chooses such measures for mixtures. Therefore the mismatch between Shannon/Gibbs entropy and von Neumann entropy follows from the framework's own premises. Saying 'use the von Neumann entropy' is, in their view, an admission that the model cannot compute the entropy from the epistemic state, confirming the no-go result.","pith_inferences":["If the theorem holds, the Harrigan-Spekkens classification scheme turns out to be a poor measuring stick for the ontic/epistemic debate: both branches of the dichotomy fail, and the dichotomy itself is the problem.","The entropy test suggests a practical diagnostic for any proposed ontological model: check whether statistical mixtures are classical measures; if they are, a Shannon-von Neumann mismatch is likely to appear in some regime.","The argument could be pressed further: the same classical-mixture assumption may undermine not just HS models but any hidden-variable program that represents quantum mixtures as classical ensembles, which is a broader target than the paper explicitly claims.","One concrete quantity to study is the gap between Shannon and von Neumann entropy for a two-state mixture; that gap quantifies exactly how much classical distinguishability the HS model wrongly adds."],"forward_implications":["A Harrigan-Spekkens psi-ontic model cannot reproduce quantum statistical mechanics, quantum thermodynamics, or quantum information theory (e.g., the Boltzmann distribution or the Holevo bound), so it cannot be a full model of quantum mechanics.","The PBR theorem, because it presupposes the Harrigan-Spekkens framework, is not evidence for a realist reading of the quantum state; it only rules out HS psi-epistemic models.","The HS framework is internally too classical: its classical mixture rule already distinguishes all ontic states, and adding more structure to hide this at the level of measurements does not fix the mixed-state entropy problem.","The no-go theorem does not rule out all realist interpretations; models like Bohmian mechanics may not satisfy the HS operational definitions, so their status is left open."],"supporting_citations":[{"why":"the paper whose no-go theorem is being defended; it supplies the original entropy calculation.","marker":"Carcassi et al. (2024)"},{"why":"defines psi-ontic and psi-epistemic models and the classical mixing rule for statistical mixtures that carries the argument.","marker":"Harrigan and Spekkens (2010)"},{"why":"the criticism under review; identifying its starting point at step 5 of the argument is what the reply contests.","marker":"Gao (2024)"},{"why":"independently identifies the same problematic issue in the HS categorization, supporting the claim that the problem is recognized.","marker":"Caticha (2022)"}],"fun_headline_variants":["No-go theorem for psi-ontic models survives Gao's critique","Gao's criticism rebuffed: no-go theorem stands","Entropy objection fails: no-go theorem for psi-ontic models","Psi-ontic no-go theorem intact after Gao's critique"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole result collapses if the Harrigan-Spekkens framework is not actually committed to representing quantum mixtures as classical probability distributions over ontic states; the paper insists the commitment is there, but that is exactly what a defender of HS would have to deny.","fun_headline_variants_meta":{"raw":{"variants":["No-go theorem for psi-ontic models survives Gao's critique","Gao's criticism rebuffed: no-go theorem stands","Entropy objection fails: no-go theorem for psi-ontic models","Psi-ontic no-go theorem intact after Gao's critique"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001234,"raw_usage":{"total_tokens":4963,"prompt_tokens":736,"completion_tokens":4227,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":352,"completion_tokens_details":{"reasoning_tokens":4154}},"tokens_in":352,"tokens_out":4227,"duration_ms":30473,"temperature":1.0,"reasoning_tokens":4154,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:51:13.647663+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Render the theorem false by constructing an explicit Harrigan-Spekkens psi-ontic model whose epistemic states are classical probability measures over ontic states and that still reproduces the von Neumann entropy of, say, an equal mixture of spin-up along z and spin-up along x (or that derives the Holevo bound). Producing such a model with its density-matrix outcome probabilities would directly contradict the no-go claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the paper whose no-go theorem is being defended; it supplies the original entropy calculation."},{"cited_title":"and Spekkens, R","cited_arxiv_id":null,"evidence_quote":"defines psi-ontic and psi-epistemic models and the classical mixing rule for statistical mixtures that carries the argument."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the criticism under review; identifying its starting point at step 5 of the argument is what the reply contests."},{"cited_title":"measure ment","cited_arxiv_id":null,"evidence_quote":"independently identifies the same problematic issue in the HS categorization, supporting the claim that the problem is recognized."}],"review_version":1}