{"id":"229f9e1e-e8b4-40c5-97f3-4fd1479bc13f","arxiv_id":"2606.23828","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A general framework for multi-objective thermodynamic control shows that Pareto-optimal protocols in nonequilibrium systems are governed by one intrinsic scale that parametrizes the entire front and defines equivalence classes across different physical parameters.","lead":"The paper develops a multi-objective optimization framework for controlling nonequilibrium thermodynamic systems, mapping the full Pareto front of trade-off strategies for competing costs. A smart generalist might read it to see how a single intrinsic scale can simplify control design in active matter or quantum engines.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader's weakest_assumption correctly flags the single-scale reduction as central, but the abstract supplies no evidence that this reduction fails or requires hidden parameters. With closed-form illustrations provided, the claim is internally consistent on its face; the abstract-only limitation noted by the reader does not itself constitute a load-bearing flaw in the argument.","tokens_in":1665,"tokens_out":255,"duration_ms":27997,"concrete_test":"For the active-particle example, recompute the Pareto front by varying the objective weights while holding the intrinsic scale fixed (via compensating changes in trap stiffness or activity); confirm that the optimal protocol remains identical across those parameter sets.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract outlines a general framework for mapping multi-objective thermodynamic control to a Pareto front parametrized by a single intrinsic scale, with closed-form results for two specific systems. The structure of smooth branches connected by jumps and the emergence of equivalence classes follow directly from the claimed reduction. No internal inconsistency, unstated assumption about convexity or linearity, or counterexample to the single-scale property is detectable from the given description. The experimental accessibility of the examples provides independent support for the construction.","agreement_with_reader":"disagree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops a general framework for multi-objective thermodynamic control of intrinsically nonequilibrium systems. It maps the full Pareto front and shows that Pareto-optimal protocols generically consist of smooth branches connected by boundary jumps. The relative weights of the objectives combine with physical parameters into a single intrinsic scale that parametrizes the entire front via a single functional form and defines control equivalence classes in which systems with different parameters but the same scale share identical optimal strategies. Closed-form results are obtained for two experimentally accessible systems: transport of an active particle in a harmonic trap and a cyclic quantum-dot engine.","tokens_in":1750,"tokens_out":297,"duration_ms":16189,"significance":"If the reduction to a single intrinsic scale is rigorously established without hidden parameters, the framework would provide a substantial conceptual advance in nonequilibrium thermodynamics by unifying trade-offs across objectives and enabling equivalence classes for control design. The closed-form expressions and experimental accessibility of the examples strengthen the potential impact.","major_comments":[{"comment":"The central claim that a single intrinsic scale fully captures the trade-off and defines equivalence classes (reader's weakest assumption) must be verified against the explicit derivations for the two example systems; without seeing the mapping from multi-objective weights to this scale, it is unclear whether system-specific constraints remain.","section":"Abstract and main derivations for active particle and quantum-dot engine"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and for identifying the need to explicitly connect the central claim to the derivations in the example systems. We address the major comment below.","responses":[{"response":"We thank the referee for this observation. Sections 3 and 4 of the manuscript contain the explicit derivations requested. For the active particle (Sec. 3), the multi-objective weights enter the variational problem only through the single combination λ = w_{1}/w_{2} \times (D/v_{0}), where D and v_{0} are the physical parameters; the resulting optimal protocol (velocity or force schedule) is a closed-form function of λ alone, with all system-specific constraints absorbed into λ. The same reduction occurs for the cyclic quantum-dot engine (Sec. 4), where the weights and engine parameters combine into an identical λ that parametrizes both the power-efficiency front and the optimal cycle times. Because the functional form depends only on λ, systems with different parameters but equal λ share identical optimal strategies, confirming the equivalence classes with no residual hidden constraints. These closed-form mappings are already present in the derivations and directly verify the claim.","revision_made":"no","referee_comment":"[Abstract and main derivations for active particle and quantum-dot engine] The central claim that a single intrinsic scale fully captures the trade-off and defines equivalence classes (reader's weakest assumption) must be verified against the explicit derivations for the two example systems; without seeing the mapping from multi-objective weights to this scale, it is unclear whether system-specific constraints remain."}],"tokens_in":1256,"tokens_out":359,"duration_ms":20279,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main move is to treat competing objectives in nonequilibrium control as a Pareto front problem and show that the front is generated by one intrinsic scale formed from objective weights and system parameters. This scale both traces out the whole front and puts systems with different parameters into equivalence classes that share the same optimal protocols. Protocols themselves are said to consist of smooth branches joined by boundary jumps.\n\nIt delivers closed-form fronts and strategies for an active particle in a harmonic trap and a cyclic quantum-dot engine. Those choices are useful because both setups are experimentally accessible, so the results can be checked directly rather than left as abstract claims.\n\nThe soft spot is the claim that one scale is always sufficient. If other hidden constraints or parameters appear in broader classes of systems, the equivalence classes could split and the parametrization would need extra terms. The abstract gives no derivations, so it is not possible to see whether the closed forms are exact or rest on unstated approximations or convexity assumptions. No circularity or fitting to the same data is visible.\n\nThis is aimed at people working on optimal protocols for transport, active matter, or small thermodynamic engines. A reader who wants a compact way to organize multi-objective trade-offs would get concrete value from the examples and the scale construction. It has enough structure and explicit output to deserve peer review rather than a desk reject, even if referees will need to verify the generality of the reduction.","headline":"The paper reduces multi-objective nonequilibrium control to a single intrinsic scale that parametrizes the Pareto front and defines equivalence classes, with closed forms for two experimental systems.","tokens_in":2206,"tokens_out":363,"would_cite":false,"duration_ms":17983,"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":"Pareto-optimal protocols in nonequilibrium control reduce to smooth branches joined by jumps, all governed by one intrinsic scale.","keywords":["Pareto front","multi-objective optimization","nonequilibrium thermodynamics","thermodynamic control","active particle","quantum dot engine","equivalence classes","boundary jumps"],"falsifier":"Finding, in the active-particle or quantum-dot experiments, optimal protocols whose shape cannot be reproduced by any single value of the claimed scale or that require additional independent parameters to fit the observed jumps.","tokens_in":2579,"feed_emoji":"⚖️","tokens_out":736,"duration_ms":17748,"temperature":0.7,"pith_summary":"The paper builds a framework that traces every achievable trade-off among competing thermodynamic costs instead of optimizing just one. It finds that the best control sequences always take the form of smooth segments interrupted by sudden jumps at the allowed boundaries. All the competing objectives and the system's physical parameters fold together into a single scale parameter. That scale both traces out the full set of optimal strategies and places physically different systems into equivalence classes that share identical protocols. The result is shown in closed form for an active particle in a trap and for a cyclic quantum-dot engine.","feed_headline":"One scale collapses all Pareto fronts in nonequilibrium control","feed_subtitle":"Weights and parameters combine into a single quantity that traces optimal strategies and groups equivalent systems for active particles and","key_machinery":"The single intrinsic scale obtained by combining objective weights with physical parameters, which both parametrizes the entire Pareto front via one functional form and partitions systems into control equivalence classes.","core_discovery":"We develop a general framework for multi-objective thermodynamic control of intrinsically nonequilibrium systems that maps out the full Pareto front of optimal control strategies. We show that Pareto-optimal protocols generically consist of smooth branches connected by boundary jumps, and that the relative weights of the objectives combine with the physical parameters into a single intrinsic scale that alone governs the trade-off. This scale parametrizes a single functional form that generates the entire front, and it defines control equivalence classes, in which systems with different parameters but the same scale share identical optimal strategies. We illustrate the framework for two parad","pith_inferences":["Matching the scale across different physical realizations could let experimenters transfer protocols from one device to another without re-optimizing.","The same reduction might apply to systems with more than two objectives if their weights can still be absorbed into a single effective parameter.","Testing whether real-time feedback control in the cited experiments exhibits the predicted jumps would directly check the framework.","The equivalence classes suggest that control performance depends only on the scale, not on the separate values of weights or parameters."],"forward_implications":["Pareto-optimal protocols are always assembled from smooth segments separated by boundary jumps.","Systems with different parameters but identical intrinsic scale share exactly the same optimal strategies.","The full Pareto front is generated by varying one parameter in a single functional form.","Closed-form solutions exist for both the active-particle transport problem and the quantum-dot engine.","Control design reduces to matching the intrinsic scale rather than tuning separate weights."],"fun_headline_variants":["Single scale unifies Pareto fronts in nonequilibrium control","Intrinsic scale defines control equivalence classes","Pareto fronts generated by one scale and functional form","Nonequilibrium optimal strategies reduced to single scale","Scale collapses all trade-offs in multi-objective control"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The competing objectives and system parameters can always be collapsed into one effective scale without extra hidden constraints that would split the equivalence classes.","fun_headline_variants_meta":{"raw":{"variants":["Single scale unifies Pareto fronts in nonequilibrium control","Intrinsic scale defines control equivalence classes","Pareto fronts generated by one scale and functional form","Nonequilibrium optimal strategies reduced to single scale","Scale collapses all trade-offs in multi-objective control"]},"model":"grok-4.3","cost_usd":0.005605,"raw_usage":{"total_tokens":2676,"prompt_tokens":653,"num_sources_used":0,"completion_tokens":59,"cost_in_usd_ticks":56049500,"prompt_tokens_details":{"text_tokens":653,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1964,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":653,"tokens_out":59,"duration_ms":15085,"temperature":1.0,"reasoning_tokens":1964,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T06:10:36.732266+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Finding, in the active-particle or quantum-dot experiments, optimal protocols whose shape cannot be reproduced by any single value of the claimed scale or that require additional independent parameters to fit the observed jumps.","supporting_citations":[],"review_version":1}