{"id":"b4459273-0334-4dd7-acbe-c33dd53ca701","arxiv_id":"2607.11704","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Heat-engine operation forces a universal Fano-factor floor of F>1/2 for fermionic coherent thermoelectric transport and F>1 for bosonic or classical carriers.","lead":"Coherent thermoelectric heat engines made of electrons cannot run with a Fano factor below 1/2; bosonic or classical ones cannot go below 1. The result tightens how much 'quantum advantage' a heat engine can claim over classical thermodynamic uncertainty bounds.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The strongest claim is a precise, mode-specific TUR for coherent two-terminal thermoelectric heat engines. The proofs are complete within scattering theory (0 ≤ T(E) ≤ 1, mean-field interactions), the bounds are shown tight by construction and by sampling, and the efficiency reformulations follow by elementary inversion. The modeling restriction noted by the reader is real but is already the paper's explicit domain of validity; it does not constitute an internal inconsistency or a hidden assumption that would falsify the stated result. No load-bearing technical flaw was found that would warrant changing the ACCEPT verdict.","tokens_in":22906,"tokens_out":463,"duration_ms":3864,"concrete_test":"Independently re-derive the fermionic bound starting from Eqs. (A1)–(A8) and the heat-engine condition P = (TH-TC)u*I > 0, confirming that the pointwise inequality g_th_S ≥ l_X(x) g_I holds for every energy and that integration recovers Eq. (3); if the tangent-line step fails for any admissible T(E), the floor F > 1/2 is not rigorous.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is internally consistent under the paper's stated modeling assumptions. The End Matter and SM proofs correctly use the heat-engine constraint (u* > 0 for I > 0) to confine energy-resolved points to the sector where y(x,u) ≥ ymin_EF(x), then apply the tangent-line argument exploiting convexity of ymin_EF for x > 0 (and the sign-flip for I < 0). The bosonic/classical case follows by Jensen from the mode-independent identity g_cl_S/|g_I| = coth(|x|). Numerical sampling with boxcar unions saturates the bounds, and the authors themselves flag multiterminal/nonthermal extensions as open. The reader's weakest_assumption correctly identifies the modeling scope but does not undermine the claim as stated for coherent two-terminal Landauer–Büttiker heat engines.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript derives heat-engine-specific thermodynamic uncertainty relations for coherent two-terminal thermoelectric transport in the Landauer–Büttiker framework. For fermions, heat-engine operation yields SI/|I| ≥ 1 + cosh^{2}(σ/(2kB|I|))/sinh(σ/(kB|I|)) (Eq. 3), implying the universal floor F > 1/2 and a refined efficiency bound (Eq. 2); a tighter temperature-resolved form (Eq. 4) holds for TH ≤ 2TC. For bosonic and classical carriers the mode-independent bound SI/|I| ≥ coth(σ/(2kB|I|)) (Eq. 5) enforces F > 1 and precludes classical-TUR violations. The bounds are obtained from energy-filter envelopes, convexity of the lower envelope ymin_EF, a tangent-line integration for arbitrary T(E), and Jensen’s inequality; multi-boxcar numerical sampling demonstrates that they are tight and saturatable.","tokens_in":23083,"tokens_out":708,"duration_ms":13904,"significance":"The central results are load-bearing for the field: they show that classical-TUR violations (often taken as a quantum advantage) are far more restricted for heat engines than for generic processes, and they introduce hard, experimentally accessible Fano floors (F > 1/2 for fermions, F > 1 for bosons/classical). The End Matter and Supplemental Material supply complete analytic proofs under the stated assumptions, the bounds are parameter-free, and the numerical saturation evidence with random boxcar unions is reproducible. The efficiency reformulations enable thermodynamic inference from electrical quantities alone. These contributions are solid and of clear interest to mesoscopic thermodynamics and quantum transport.","major_comments":[],"minor_comments":[{"comment":"Fig. 3 caption and main-text discussion of the scatter plots would benefit from a brief statement of the sampled ranges for TH/TC, δμ and boxcar parameters, so that readers can judge coverage of the large-dissipation regime.","section":null},{"comment":"End Matter, after Eq. (A8): the relation u(E) = u* + τ x(E) is central; a short sentence reminding the reader that u* is energy-independent would improve readability for non-specialists.","section":null},{"comment":"The phrase “quantum advantage” (green shaded region in Fig. 2) is used for classical-TUR violation; a parenthetical clarification that this refers only to the charge-current Fano factor would avoid possible misreading.","section":null},{"comment":"Supplemental Material S1.C (maximum-power comparison) is useful but could be cross-referenced more explicitly in the main text when the F > 1/2 floor is discussed.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is a clean, self-contained advance that fits well in a high-impact condensed-matter or quantum-thermodynamics venue. The modeling assumptions (two-terminal coherent LB) are stated clearly and the open extensions are flagged honestly; I see no novelty or citation concerns."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The real news here is a heat-engine-specific charge-current TUR for coherent two-terminal transport. For fermions it tightens Brandner–Saito to SI/|I| ≥ 1 + cosh²(σ/2kB|I|)/sinh(σ/kB|I|), which forces F > 1/2 and confines classical-TUR violations to a few percent in a narrow window of entropy production. For bosons and classical carriers the bound is SI/|I| ≥ coth(σ/2kB|I|), so F > 1 and the classical Markov TUR is never violated. The associated efficiency bounds follow immediately and are electrically measurable.\n\nWhat they do well: the End Matter and SM give complete analytic arguments—energy-filter envelopes, convexity of ymin_EF, tangent-line integration for arbitrary T(E) under the heat-engine constraint u* > 0, and Jensen for the bosonic/classical case. The multi-boxcar scatter plots populate the allowed region and approach the bound even at large dissipation; data are on Zenodo. Citations are appropriate and the recovery of Brandner–Saito when the heat-engine constraint is dropped is clean.\n\nSoft spots are modest and mostly scoped by the authors themselves. The derivation lives inside two-terminal coherent Landauer–Büttiker with mean-field interactions; inelastic scattering, strong correlations, or extra terminals could move occupations outside the (x,u) sectors that make the pointwise envelope work. That is a real modeling boundary, not a hidden flaw in the math. The temperature-resolved bound for TH ≤ 2TC is a nice extra, but the main floor F > 1/2 is the headline result.\n\nThis is for people working on quantum TURs and mesoscopic thermoelectrics who care about precision–efficiency trade-offs. The central claim holds under the stated assumptions, the proofs are reproducible, and the numerics support tightness. I would send it to peer review without hesitation; it is a solid, useful advance inside its domain.","headline":"Clean, mode-specific TUR that forces F > 1/2 for fermionic coherent heat engines (and F > 1 for bosons/classical); proofs and numerics look solid under the stated Landauer–Büttiker assumptions.","tokens_in":23717,"tokens_out":536,"would_cite":true,"duration_ms":4855,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Any coherent fermionic thermoelectric heat engine must have charge-current Fano factor above 1/2; bosons and classical carriers sit above 1.","keywords":["thermodynamic uncertainty relation","Fano factor","coherent thermoelectric heat engine","Landauer-Büttiker transport","charge-current noise","quantum advantage","bosonic transport"],"falsifier":"Fabricate a two-terminal coherent fermionic heat engine (or a numerical transmission) whose measured charge-current Fano factor falls below 1/2 while still producing positive power, or a bosonic engine whose Fano factor falls below 1.","tokens_in":23805,"feed_emoji":"⚡","tokens_out":960,"duration_ms":11191,"temperature":0.7,"pith_summary":"Thermodynamic uncertainty relations say that driving a current with low noise costs high dissipation. For coherent two-terminal thermoelectric heat engines the paper tightens that trade-off by restricting the process to heat-engine operation. For fermions the resulting bound forces the Fano factor of the charge current to stay above one-half; classical Markovian violations, often taken as a quantum advantage, are confined to a narrow window of entropy production and remain only a few percent. For bosons and classical carriers the floor rises to one and the classical relation is never broken. The bounds are shown to be tight by random sampling of boxcar transmissions that reach the predicted floors, and they convert into efficiency bounds that require finite fluctuations to run at nonzero efficiency. The result therefore tells experimentalists what electrical noise floor is unavoidable when a mesoscopic conductor is used as a heat engine.","feed_headline":"Heat engines cannot run quieter than Fano factor 1/2","feed_subtitle":"Coherent fermionic thermoelectrics hit a hard noise floor; bosons and classical carriers sit twice as high.","key_machinery":"The energy-resolved lower envelope ymin_EF(X) = (1 + cosh^{2}X)/sinh(2X) obtained for a perfect energy filter under the heat-engine constraint |u| ≥ |x|; convexity of this envelope supplies a tangent-line inequality that integrates against an arbitrary transmission to give the global Fano-factor bound.","core_discovery":"Selecting heat-engine operation for fermionic coherent thermoelectric transport produces a charge-current thermodynamic uncertainty relation whose right-hand side approaches 1/2 at large dissipation, so every such engine obeys F > 1/2. The same selection for bosonic or classical carriers yields a mode-independent bound that approaches 1, so F > 1 and the classical Markov TUR is never violated.","pith_inferences":["If multiterminal or nonthermal reservoirs can evade the two-terminal (x,u) sector constraint, the F > 1/2 floor becomes a diagnostic of how close a device stays to ideal two-terminal coherence.","The same tangent-line technique may tighten other working-mode-specific figures of merit (cooling power precision, accelerator noise) once the corresponding sector geometry is mapped.","Because the bounds are saturated by simple boxcar filters, they give an immediate design target for engineered energy-selective transmissions in cold-atom or molecular thermoelectric platforms."],"forward_implications":["A coherent fermionic heat engine cannot reach finite efficiency with vanishing charge-current fluctuations; SP must stay at least δµP/2.","Classical-TUR violations available to a fermionic heat engine are limited to roughly 6.8 percent and only inside a narrow window of entropy production.","When TH ≤ 2 TC the fermionic floor jumps from 1/2 to 1 and quantum advantage disappears entirely.","Efficiency can be bounded from electrical measurements alone (Fano factor and voltage bias) without measuring heat currents.","Bosonic and classical ballistic engines share the same stricter bound F > 1 and never beat the classical Markov TUR."],"fun_headline_variants":["Fermionic heat engines face hard Fano floor above 1/2","Coherent fermionic thermoelectrics bound charge Fano factor >1/2","Heat-engine mode forces fermionic Fano factor above one half","Bosonic and classical carriers lift heat-engine Fano limit to 1","TUR for fermionic engines approaches F>1/2 at high dissipation"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"Everything rests on two-terminal coherent transport fully described by Landauer–Büttiker scattering with transmissions between zero and one; inelastic scattering, strong correlations, or extra terminals could open occupations outside the constrained sectors and drop the Fano factor below the claimed floors.","fun_headline_variants_meta":{"raw":{"variants":["Fermionic heat engines face hard Fano floor above 1/2","Coherent fermionic thermoelectrics bound charge Fano factor >1/2","Heat-engine mode forces fermionic Fano factor above one half","Bosonic and classical carriers lift heat-engine Fano limit to 1","TUR for fermionic engines approaches F>1/2 at high dissipation"]},"model":"grok-4.5","effort":"low","cost_usd":0.005214,"raw_usage":{"total_tokens":1347,"prompt_tokens":669,"num_sources_used":0,"completion_tokens":85,"cost_in_usd_ticks":52140000,"prompt_tokens_details":{"text_tokens":669,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":593,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":669,"tokens_out":85,"duration_ms":4838,"temperature":1.0,"reasoning_tokens":593,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T03:43:58.848593+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Fabricate a two-terminal coherent fermionic heat engine (or a numerical transmission) whose measured charge-current Fano factor falls below 1/2 while still producing positive power, or a bosonic engine whose Fano factor falls below 1.","supporting_citations":[],"review_version":1}