{"id":"17d8ad5c-3859-466b-b907-5417c11f85d8","arxiv_id":"2502.07917","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"A universal inequality (S/J) sinh[sigma/(2 k_B J)] >= 1 is derived for time-reversal-symmetric coherent fermionic transport, with a weakened factor for broken time-reversal symmetry.","lead":"The paper derives a new thermodynamic uncertainty relation for coherent fermionic transport, bounding entropy production by the mean and fluctuations of a single particle current. It extends the bound to broken time-reversal symmetry and applies it to thermoelectric engine and refrigerator efficiency trade-offs.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reservoir-only entropy balance in Eq. (9) restricts the bound to systems without internal dissipation, limiting its practical scope.","rationale":"I checked the derivation of Eq. (2) step by step. The convexity argument for Phi, the AM-GM bound leading to 2N_alpha <= Sth_alpha <= S_alpha, the antisymmetry of arsinh for negative currents, and the rearrangement into Eq. (2) are all mathematically sound within the stated coherent-transport model. The internal-dissipation limitation is the weakest point of the practical claim because Eq. (9) is the definition of sigma used throughout. The paper's probe-terminal robustness argument is not a proof, and the paper itself labels it as an expectation. This concern does not invalidate the central inequality for ideal coherent conductors, but it makes the claim conditional for real systems. The numerical constant psi_0 in the broken-TRS bound and the finite-N verification of the quantum-dot transmission function are secondary; they do not affect Eq. (2). Therefore I agree with the reader's identification of the reservoir-only entropy balance as the load-bearing assumption, and the verdict remains CONDITIONAL.","tokens_in":12305,"tokens_out":30705,"duration_ms":247792,"concrete_test":"Numerically test the bound in a two-terminal coherent conductor coupled to an additional Büttiker probe held at a fixed temperature, allowing a nonzero heat current into the probe to model phonon-induced dissipation. Using the full scattering matrix, compute the total entropy production sigma_total = -Q_1/T_1 - Q_2/T_2 - Q_p/T_p and the current J_1 and noise S_1 in one physical terminal. Vary the probe temperature and bias; if Q_qu = (S_1/J_1) sinh[sigma_total/(2k_B J_1)] ever falls below 1, the bound does not extend to internal dissipation. If no violations occur across a wide parameter range, the robustness expectation gains numerical support.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The derivation of Eq. (2) depends on Eq. (9), which identifies the total entropy production rate with the sum of reservoir heat currents divided by reservoir temperatures. This is exact only when no entropy is generated inside the sample, i.e., for perfectly coherent, non-interacting transport. The paper's second remark claims that probe terminals can model incoherent or inelastic scattering and that the bound is therefore robust against internal dissipation, but this is stated as an expectation, not derived. A probe with zero average heat and particle current can simulate elastic dephasing, but genuine inelastic dissipation requires a nonzero heat flow into the probe (or a separate bath), which would add a positive contribution to sigma. Hence, applying Eq. (2) to real devices with interactions or phonon coupling could underestimate the total entropy production. The paper itself acknowledges this gap by saying 'We therefore expect', which is why the central claim, while correct within the coherent-transport model, is not established for the broader physical setting claimed in the discussion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives a universal thermodynamic uncertainty relation for fermionic coherent transport, Eq. (2): Q_qu = (S_alpha/J_alpha) sinh[sigma/(2 k_B J_alpha)] >= 1, where J_alpha and S_alpha are the mean and zero-frequency fluctuations of the particle current entering terminal alpha and sigma is the total rate of entropy production. The proof uses Landauer-Buttiker expressions for currents and noise, rewrites sigma as an integral of a convex function x arsinh x, applies a tangent bound, and eliminates the channel-overlap factor N_alpha using the AM-GM inequality. The paper also gives a broken-time-reversal version with a numerical constant psi_0, derives power-efficiency-fluctuation trade-offs for heat engines and refrigerators, and illustrates the results with a quantum dot chain whose transmission function approaches a boxcar shape.","tokens_in":12532,"tokens_out":39682,"duration_ms":333618,"significance":"The central result is significant: it provides a parameter-free lower bound on dissipation from a single measured current and its noise, valid arbitrarily far from equilibrium and for arbitrary multi-terminal geometries, and it is tight for narrow boxcar transmissions. The derivation is elegant and self-contained, and the thermoelectric trade-off relations are practically useful. The main limitations are the restriction to non-interacting coherent transport without internal dissipation and the reliance of the broken-TRS extension on a numerically determined constant rather than a fully analytic proof.","major_comments":[{"comment":"The claim that Eq. (2) 'still applies' to systems with incoherent or inelastic scattering and interactions through probe terminals is not derived. The entropy balance sigma = -sum_alpha Q_alpha/T_alpha is exact only when no entropy is produced inside the sample; a probe with zero net particle and heat current can model elastic dephasing but not inelastic dissipation, which requires a nonzero heat flow into the probe and therefore adds a positive contribution to sigma. Since the paper only states 'we expect' robustness, this passage should be explicitly labeled as a conjecture, or a proof should be given that the probe heat contribution cannot make the bound fail.","section":"Section 2 (second remark) and Eq. (9)"},{"comment":"The broken-time-reversal bound Eq. (16) rests on the numerical statement psi[x,y] >= psi_0 = 0.85246 over [0,1]^2. No analytical certificate or interval-arithmetic verification is provided, so the advertised extension to systems with broken time-reversal symmetry is not fully proven. In addition, the step from the psi_0 replacement to Eq. (16) is only sketched ('along the lines described in the main text'), although the variable Y = (f_alpha - f_beta)/(g_alphaalpha + g_betabeta) and the weight differ from the time-reversal-symmetric case; the cancellation condition is Y_0 = J_alpha/S_th^alpha. Please provide a rigorous lower bound on psi and spell out the analog of the tangent argument.","section":"Supplemental Material, Eq. (S5) and Eq. (16)"},{"comment":"The derivation requires g^alpha_beta_E = f^alpha_E(1 - f^beta_E) > 0, which holds only for finite reservoir temperatures. At T = 0 the quantities N_alpha and S_alpha can vanish while J_alpha stays nonzero (for example, a perfectly transmitting channel), so Eq. (2) as written is not defined and the proof's tangent argument breaks down. The theorem should be stated for finite reservoir temperatures, with the zero-temperature limit discussed separately.","section":"Eq. (2) and surrounding statement"}],"minor_comments":[{"comment":"The ratios S_alpha/J_alpha are written without absolute values; for J_alpha < 0 the expression is nevertheless positive because the hyperbolic sine has the same sign as J_alpha. To avoid confusion for the reader, it would be clearer to write |J_alpha| in the prefactor.","section":"Eqs. (2) and (16)"},{"comment":"The numerical minimization of psi is not documented; please state the method (grid size, precision, or certified interval arithmetic) or provide the code or data used to obtain psi_0.","section":"Supplemental Material, after Eq. (S5)"},{"comment":"The notation 'iGamma = t0 = tN' appears to contain a typo; presumably t0 and tN denote boundary hopping amplitudes and the reservoir coupling is Gamma. Please clarify the notation.","section":"Eq. (24)"},{"comment":"The cases J_alpha = 0 and zero temperature are not discussed; the inequality is singular in both cases, and the limiting statements should be made precise if these cases are meant to be included.","section":"Eq. (2) and limiting cases"}],"recommendation":"major_revision","confidential_remarks":"The central derivation of Eq. (2) appears sound and the paper is well within the scope of the journal. The revisions I request concern the scope claim about probe terminals and the rigor of the broken-TRS constant; both are local and should be addressable without changing the main result."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper derives a universal thermodynamic uncertainty relation for coherent fermionic transport, Eq. (2), and the derivation is solid. The proof is simple and elegant: rewrite the entropy production as a sum of nonnegative terms, use convexity of x·arsinh x, and apply the AM-GM bound to relate thermal noise to the conductance. There are no fitted parameters, and the result is genuinely new for multi-terminal geometries and arbitrary biases. The two-terminal boxcar saturation was already known (Ref. 45), but the general bound and the engine trade-off relations are new. What the paper does well: the argument is transparent and self-contained. The broken-time-reversal extension uses a numerically minimized constant psi_0 ≈ 0.85246, but they also give a rational lower bound 17/20, so even without a formal certificate it is on firm ground. The quantum-dot chain transmission function (25) was checked by computer algebra for N=1..10 and numerically for N=11..100, which is reproducible evidence. The trade-off relations for heat engines and refrigerators are a concrete and useful application. Soft spots: the claim that the bound remains valid in the presence of inelastic scattering or interactions via probe terminals is stated as an expectation, not derived. That is a real gap if you want to apply the bound to devices with internal dissipation, but it does not undercut the core result. The bound is derived for coherent transport, where the entropy balance in Eq. (9) is exact. Moreover, since any internal dissipation only adds to the total entropy production, the bound on the reservoir entropy production automatically bounds the total. So the practical inference application is actually unaffected. The numerically minimized psi_0 without a formal certificate is a minor concern, especially because they provide a safe rational lower bound. Who this is for: researchers in mesoscopic transport and quantum thermodynamics. The paper deserves a serious referee; the main theorem is new and correct within its stated regime, and the applications are concrete. I would send it to review rather than desk reject.","headline":"A clean, self-contained derivation of a universal TUR for coherent fermionic transport; the main bound holds, with minor caveats about the broken-TRS constant and the probe-terminal claims.","tokens_in":644,"tokens_out":611,"would_cite":true,"duration_ms":33780,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C05","82C70"],"pacs":[],"model":"deepseek-v4-flash","headline":"For coherent fermionic conductors, the entropy-production rate is bounded from below by a measured current and its fluctuations, through the inequality Q_qu ≥ 1, which holds at arbitrary bias in any multi-terminal geometry.","keywords":["thermodynamic uncertainty relation","coherent transport","entropy production","current fluctuations","Landauer-Büttiker formalism","shot noise","thermoelectric efficiency","quantum dot chain"],"falsifier":"Construct a multi-terminal fermionic conductor with time-reversal-symmetric scattering but with finite interactions or inelastic collisions inside the sample, then measure J_α, S_α, and the true total entropy production, and check whether the quantity (S_α/J_α) sinh[σ/(2 k_B J_α)] drops below 1 wherever those internal processes dissipate energy.","tokens_in":12119,"feed_emoji":"⚡","tokens_out":4880,"duration_ms":43843,"temperature":0.7,"pith_summary":"The paper establishes a thermodynamic uncertainty relation for coherent (ballistic, non-interacting) fermionic transport through a multi-terminal sample. It proves that at any terminal α, the combination Q_qu = (S_α/J_α) sinh[σ/(2 k_B J_α)] is always at least 1, where J_α is the mean particle current entering from that terminal, S_α is its full fluctuation (thermal plus shot noise), and σ is the total entropy-production rate. The bound holds for arbitrary chemical and thermal biases, any number of terminals, and any scattering potential, as long as the microdynamics are symmetric under time reversal. It is tight: a two-terminal conductor with a boxcar-shaped transmission function saturates it. This gives a practical way to lower-bound total dissipation from a single measured current and its noise, without measuring heat currents.","feed_headline":"Noise sets the dissipation floor for coherent conductors","feed_subtitle":"A single measured current and its fluctuations bound entropy production at any bias, with no heat-current measurement needed.","key_machinery":"The load-bearing object is the inequality Q_qu = (S_α/J_α) $\\sinh$[σ/(2 k_B J_α)] ≥ 1, derived through the scattering formalism. The proof rewrites the entropy production σ in terms of transmission functions and Fermi functions, introduces the convex function Φ[x] = x·arsinh(x), applies a tangent-line (Jensen) bound at an optimally chosen point X = J_α/(2N_α), and then uses the relation S_α ≥ 2N_α ≥ S_α^th to eliminate the auxiliary quantity N_α. For broken time-reversal symmetry, a similar argument with a concavity bound on the binary entropy function yields the same form with the numerical factor ψ_0 ≃ 0.85246 inserted into the argument of the hyperbolic sine.","core_discovery":"The central discovery is that, for fermionic coherent conductors, the classical thermodynamic uncertainty relation Q_cl = σS/(2 k_B $J^{2}$) ≥ 1 is replaced by Q_qu = (S_α/J_α) $\\sinh$[σ/(2 k_B J_α)] ≥ 1. Unlike its classical counterpart, this inequality is never violated by energy filtering and Pauli blocking; it holds arbitrarily far from equilibrium and for any multi-terminal geometry. The proof uses only the Landauer–Büttiker scattering formalism, the reservoir-only entropy balance σ = −∑_α Q_α/T_α, and convexity of x·arsinh(x). In linear response, the hyperbolic sine linearizes and the classical bound is recovered; with a numerical prefactor ψ_0 ≃ 0.85246, the bound extends to samples with broken time-reversal symmetry.","pith_inferences":["Beyond the paper: if the probe-terminal expectation holds, the bound could serve as a general dissipation-inference tool for interacting quantum dot arrays, where heat currents are hard to measure.","Beyond the paper: the appearance of the symmetry-dependent prefactor ψ_0 suggests a possible family of uncertainty relations with prefactors tied to the degree of time-reversal breaking, which could be explored numerically for partially symmetric scattering matrices.","Beyond the paper: the tightness at boxcar transmission profiles invites searches for finite-parameter transmission shapes that nearly saturate the bound at small N, potentially guiding the design of high-precision, low-dissipation mesoscopic devices.","Beyond the paper: the same convexity-based proof strategy might extend to heat-current fluctuations, although the paper notes that an additional parameter would be needed to match physical dimensions."],"forward_implications":["A two-terminal thermoelectric heat engine obeys the trade-off relation Q_qu^HE ≥ 1, implying that ideal Carnot efficiency is attainable only with vanishing power output or diverging power fluctuations.","A two-terminal thermoelectric refrigerator satisfies a similar trade-off, and its efficiency can be estimated from current mean and fluctuations alone, bypassing difficult heat-current measurements.","A chain of quantum dots with specially tuned hopping amplitudes and reservoir couplings produces a nearly boxcar transmission function, essentially saturating the quantum bound while strongly violating the classical one.","The bound extends to time-reversal-broken systems, including chiral quantum Hall edge states, at the cost of only a numerical factor ψ_0 in the dissipation estimate.","The authors expect (but do not prove) that the bound remains robust against moderate dephasing, internal dissipation, and carrier interactions when these are modeled by probe terminals.","In the linear-response limit, the bound reduces exactly to the classical thermodynamic uncertainty relation, showing that violations of the classical bound are a far-from-equilibrium effect."],"supporting_citations":[{"why":"Supplies the Landauer–Büttiker scattering formalism, the expressions for mean currents, thermal noise, shot noise, and the unitarity/current-conservation sum rules used throughout.","marker":"[42-44]"},{"why":"Defines the classical thermodynamic uncertainty relation for Markov jump processes that the new bound generalizes and improves upon.","marker":"[5]"},{"why":"Establishes that dissipation bounds all steady-state current fluctuations classically, providing the baseline intuition that the quantum bound extends.","marker":"[6]"},{"why":"Earlier observation that a boxcar transmission function yields equality in the quantum bound and exponential suppression of current fluctuations, which is the starting point for the tightness claim.","marker":"[45]"},{"why":"Gives the classical trade-off relations between power, efficiency, and constancy in heat engines, which the paper extends to coherent conductors.","marker":"[4]"},{"why":"Proposes probe terminals as effective descriptions of inelastic scattering and interactions, which the paper invokes to argue for robustness beyond purely coherent transport.","marker":"[61]"},{"why":"Contains the supplemental derivations that make the steps from entropy production to the final inequality rigorous, including the broken-time-reversal case.","marker":"[62]"},{"why":"Provides the strict positivity of entropy production and the concavity argument used in the broken-time-reversal-symmetry extension.","marker":"[63]"}],"fun_headline_variants":["Quantum noise sets entropy floor for coherent transport","Current noise pins dissipation floor in coherent conductors","Entropy production bounded by current fluctuations in coherent transport","Coherent transport: current noise bounds dissipation","Noise floor for entropy production in coherent conductors"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof assumes that all entropy is produced in the reservoirs, so no inelastic scattering or interactions inside the sample generate additional dissipation; if they do, the bound constrains only the reservoir part and may miss the physically relevant total entropy production.","fun_headline_variants_meta":{"raw":{"variants":["Quantum noise sets entropy floor for coherent transport","Current noise pins dissipation floor in coherent conductors","Entropy production bounded by current fluctuations in coherent transport","Coherent transport: current noise bounds dissipation","Noise floor for entropy production in coherent conductors"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000717,"raw_usage":{"total_tokens":3177,"prompt_tokens":853,"completion_tokens":2324,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":469,"completion_tokens_details":{"reasoning_tokens":2255}},"tokens_in":469,"tokens_out":2324,"duration_ms":15186,"temperature":1.0,"reasoning_tokens":2255,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T11:26:09.352446+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a multi-terminal fermionic conductor with time-reversal-symmetric scattering but with finite interactions or inelastic collisions inside the sample, then measure J_α, S_α, and the true total entropy production, and check whether the quantity (S_α/J_α) sinh[σ/(2 k_B J_α)] drops below 1 wherever those internal processes dissipate energy.","supporting_citations":[{"cited_title":"B¨ uttiker, Scattering theory of current and intensity noise correlations in conductors and wave guides, Phys","cited_arxiv_id":null,"evidence_quote":"Proposes probe terminals as effective descriptions of inelastic scattering and interactions, which the paper invokes to argue for robustness beyond purely coherent transport."},{"cited_title":"Brandner, T","cited_arxiv_id":null,"evidence_quote":"Provides the strict positivity of entropy production and the concavity argument used in the broken-time-reversal-symmetry extension."}],"review_version":1}