{"id":"7ed5ba0b-92a4-4b2a-b72e-48153bd3d82e","arxiv_id":"2605.26687","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For specific 2D Riemann data the self-similar solution fails the maximal entropy production principle, and entropy-admissible weak solutions exist with arbitrary non-decreasing total entropy profiles.","lead":"The paper shows that for certain 2D Riemann initial data, the standard self-similar solution to the Euler gas dynamics equations fails to maximize entropy production rate. A smart generalist might read it to see why a proposed selection principle for ill-posed fluid equations does not recover the intuitively physical solution.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption concerns physical relevance of MEP, yet the paper's claim is purely that MEP fails to select the self-similar solution; the paper does not posit that MEP is the correct selection principle. The abstract-only review explains the UNVERDICTED verdict, but the stated results contain no internal inconsistency or unsupported step that would alter the verdict once the full text is examined.","tokens_in":1595,"tokens_out":287,"duration_ms":46530,"concrete_test":"Extract the explicit Riemann data and the entropy-production functional used in the first example; recompute the production rate of the self-similar solution and compare it with the rate realized by any solution whose total entropy profile strictly exceeds that of the self-similar solution on a positive-measure time interval.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a direct mathematical statement: for specific 2-D Riemann data the 1-D self-similar solution does not attain the supremum of entropy production rate among entropy-admissible weak solutions. The abstract supplies an explicit counter-example together with a general construction (arbitrary non-decreasing total entropy profiles) that immediately implies the self-similar profile cannot be maximal. No hidden assumption that MEP must be physically meaningful or must recover the self-similar solution is required for this negative result.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The paper uses convex integration to address selection of weak solutions to the 2D Euler system of gas dynamics under the entropy inequality. For specific Riemann initial data it constructs an explicit counter-example showing that the standard 1-D self-similar solution does not attain the supremum of the entropy production rate. It further proves that, for a large class of initial data, entropy-admissible weak solutions exist whose total entropy profile can be any prescribed non-decreasing function.","tokens_in":1690,"tokens_out":455,"duration_ms":23776,"significance":"If the constructions are correct, the work supplies a mathematically rigorous negative answer to whether the maximal entropy production principle recovers the intuitively physical self-similar solution, and demonstrates that the admissible entropy profiles are essentially arbitrary. The explicit counter-example and the flexible profile construction are concrete contributions to the literature on ill-posedness and selection criteria for hyperbolic systems.","major_comments":[{"comment":"§3 (counter-example construction): the verification that the self-similar solution fails to maximize the entropy production rate relies on an explicit comparison of total entropy production; the argument would be strengthened by an explicit formula or numerical value for the production rate attained by the self-similar solution versus the constructed competitor.","section":"§3"},{"comment":"Theorem 1.2 (arbitrary entropy profiles): the statement that any non-decreasing profile is attainable is load-bearing for the second claim; the proof sketch in §4 should clarify how the convex-integration scheme controls the integrated entropy production while preserving the entropy inequality pointwise.","section":"Theorem 1.2"}],"minor_comments":[{"comment":"The notation for the entropy production rate functional is introduced without a numbered equation; adding an explicit definition (e.g., Eq. (2.3)) would improve readability.","section":"§2"},{"comment":"Figure 1 (Riemann data diagram) lacks axis labels and a caption explaining the wave configuration; this is a minor clarity issue.","section":"Figure 1"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading, the positive assessment of the work, and the recommendation for minor revision. We address each major comment below.","responses":[{"response":"We thank the referee for this constructive suggestion. The comparison in §3 already establishes that the convex-integration competitor attains a strictly higher total entropy production rate than the self-similar solution, but we agree that an explicit formula or numerical illustration would make the distinction more transparent. In the revised manuscript we will add the explicit entropy-production formula for the self-similar Riemann solution together with a direct numerical comparison against the rate realized by the constructed weak solution.","revision_made":"yes","referee_comment":"[§3] §3 (counter-example construction): the verification that the self-similar solution fails to maximize the entropy production rate relies on an explicit comparison of total entropy production; the argument would be strengthened by an explicit formula or numerical value for the production rate attained by the self-similar solution versus the constructed competitor."},{"response":"We agree that additional detail on this point will strengthen the exposition. In the revised version we will expand the proof sketch in §4 to explain precisely how the convex-integration iteration is modified so that the integrated entropy production can be prescribed arbitrarily (subject only to monotonicity) while the entropy inequality is enforced pointwise at every stage of the construction.","revision_made":"yes","referee_comment":"[Theorem 1.2] Theorem 1.2 (arbitrary entropy profiles): the statement that any non-decreasing profile is attainable is load-bearing for the second claim; the proof sketch in §4 should clarify how the convex-integration scheme controls the integrated entropy production while preserving the entropy inequality pointwise."}],"tokens_in":1250,"tokens_out":381,"duration_ms":25443,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that for certain 2D Riemann data the usual 1D self-similar solution does not attain the supremum of entropy production among entropy-admissible weak solutions, and that solutions with any non-decreasing total entropy profile can be built.\n\nThe paper applies convex integration to produce both the explicit counterexample and the general existence statement. This is a natural next step after earlier non-uniqueness results for the Euler system, and it directly tests the maximal entropy production principle as a selection criterion. The negative result stands on its own without assuming the principle must be physically meaningful or must recover the self-similar solution.\n\nThe constructions look standard for this literature and the abstract plus stress-test note give no sign of circularity or hidden fitting. The only soft spot is that the technical details of the integration scheme are not visible here, so the proofs need checking in the full text; that is routine for this type of work rather than a load-bearing flaw.\n\nThe paper is for people working on ill-posedness and selection principles in hyperbolic conservation laws. A reader following the convex-integration approach to the Euler equations will get concrete information from it. It deserves a serious referee because it supplies an explicit negative instance for a proposed criterion together with a general existence statement.","headline":"The paper gives a direct 2D Riemann counterexample showing the self-similar solution does not maximize entropy production, plus a general construction for arbitrary non-decreasing entropy profiles.","tokens_in":2174,"tokens_out":339,"would_cite":false,"duration_ms":24799,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"The maximal entropy production principle excludes the standard self-similar solution for certain two-dimensional Riemann problems in the Euler system.","keywords":["Euler equations","entropy production","weak solutions","Riemann problem","convex integration","gas dynamics","maximal entropy production"],"falsifier":"A direct numerical or experimental measurement, for the specific Riemann data of the example, of whether the observed entropy production rate equals the rate of the self-similar solution or exceeds it.","tokens_in":2516,"feed_emoji":"","tokens_out":568,"duration_ms":27753,"temperature":0.7,"pith_summary":"The paper tests whether the maximal entropy production principle can select physically relevant weak solutions to the Euler equations when the entropy inequality alone fails to do so. For a specific family of two-dimensional Riemann initial data the usual self-similar solution does not maximize the entropy production rate. The authors therefore conclude that the principle eliminates the solution that appears physically natural. They also construct, for a wide class of initial data, entropy-admissible weak solutions whose total entropy can follow any prescribed non-decreasing function of time.","feed_headline":"Entropy maximization rules out self-similar Euler solutions","feed_subtitle":"For certain 2D Riemann data the principle eliminates the standard solution and allows arbitrary nondecreasing entropy profiles.","key_machinery":"The maximal entropy production principle, which selects among entropy-admissible weak solutions the one that maximizes the instantaneous rate of entropy increase.","core_discovery":"For Riemann initial data in two space dimensions the standard self-similar solution fails to attain the maximal possible rate of entropy production among entropy-admissible weak solutions. Hence the maximal entropy production principle rules out this solution. In addition, for a large class of initial data there exist entropy-admissible weak solutions whose integrated entropy production can be prescribed as any non-decreasing function of time.","pith_inferences":["Alternative selection mechanisms beyond maximal entropy production may be required to isolate physically observed solutions.","The freedom to choose the entropy profile suggests that dissipative effects in the model can be tuned independently of the initial data."],"forward_implications":["The self-similar solution is excluded by the maximal entropy production principle for the constructed two-dimensional Riemann data.","Entropy-admissible weak solutions with arbitrarily prescribed non-decreasing total entropy profiles exist for a broad class of initial data.","The non-uniqueness of weak solutions persists even after imposing the maximal entropy production criterion."],"fun_headline_variants":["Max entropy production rules out self-similar Euler solutions","Self-similar solutions fail maximal entropy production test","Euler system allows any nondecreasing entropy production profile","Riemann solutions ruled out by entropy maximization principle"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The maximal entropy production principle is a physically meaningful selection criterion that should recover the intuitively relevant self-similar solution for the given Riemann data.","fun_headline_variants_meta":{"raw":{"variants":["Max entropy production rules out self-similar Euler solutions","Self-similar solutions fail maximal entropy production test","Euler system allows any nondecreasing entropy production profile","Riemann solutions ruled out by entropy maximization principle"]},"model":"grok-4.3","cost_usd":0.0039,"raw_usage":{"total_tokens":1951,"prompt_tokens":567,"num_sources_used":0,"completion_tokens":59,"cost_in_usd_ticks":38999500,"prompt_tokens_details":{"text_tokens":567,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1325,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":567,"tokens_out":59,"duration_ms":14726,"temperature":1.0,"reasoning_tokens":1325,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T17:31:21.352546+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct numerical or experimental measurement, for the specific Riemann data of the example, of whether the observed entropy production rate equals the rate of the self-similar solution or exceeds it.","supporting_citations":[],"review_version":1}