{"id":"dce6337f-68e7-4093-acc4-878805acbf46","arxiv_id":"2606.27012","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"Odd mobility in a two-temperature Brownian dimer produces handed correlations between particles and increases thermal conductance without altering net heat flow or dissipation under handedness reversal.","lead":"The study examines a Brownian dimer of two harmonically trapped particles coupled by a spring and connected to reservoirs at different temperatures, incorporating odd mobility that turns conservative forces into transverse motion. This generates handed inter-particle correlations and circulating probability currents that enhance thermal conductance while leaving net heat current and total dissipation unchanged under reversal of the odd response.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Odd mobility inserted directly into overdamped Langevin equations without microscopic derivation or consistency check for two-temperature case","rationale":"The reader's weakest_assumption correctly isolates the single modeling step on which every subsequent analytic result depends. Because the paper presents an exact solution built on that step, confirming or refuting the consistency of the odd-mobility insertion is the decisive test; no other internal inconsistency is visible from the given material.","tokens_in":1735,"tokens_out":345,"duration_ms":9052,"concrete_test":"Start from an underdamped dimer with an explicit odd force (e.g., Lorentz force from a uniform magnetic field) and two distinct friction coefficients, perform the overdamped limit while keeping the two temperatures, and extract the effective mobility matrix; compare its antisymmetric block to the one postulated in the paper. If the extracted odd coefficients are either temperature-dependent or accompanied by additional drift terms absent from the model, the direct-addition assumption fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The model begins by writing the overdamped equations with an added antisymmetric mobility matrix that converts the harmonic forces into transverse velocities. For a two-temperature system this step requires that the antisymmetric coefficients remain compatible with the position-dependent diffusion matrix (different temperatures on each particle) and that the resulting Fokker-Planck operator still admits a normalizable stationary density whose currents can be unambiguously partitioned into irreversible and handed parts. No derivation from an underdamped Hamiltonian or explicit verification that the odd term does not generate spurious divergences or violate local detailed balance is supplied; the exact solution and the claims about enhanced conductance and reversal invariance therefore rest on this unexamined modeling assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript investigates a two-temperature Brownian dimer with odd mobility (antisymmetric transport coefficients) added to the overdamped Langevin equations. It claims an exact solution yielding analytical expressions for steady-state currents (split into irreversible and handed parts), heat transfer, and entropy production. Key results are that odd mobility generates handed particle correlations (reversing with odd handedness) while keeping individual distributions isotropic, and that it enhances thermal conductance between reservoirs without changing net heat current or total dissipation under reversal.","tokens_in":1891,"tokens_out":509,"duration_ms":34566,"significance":"If the modeling assumptions hold, the work supplies a solvable paradigm linking temperature imbalance, elastic coupling, and odd mobility to circulating currents and modified conductance, with explicit analytical expressions for observables. The exact solvability and the reversal-invariance result are notable strengths that could serve as a benchmark for odd nonequilibrium transport.","major_comments":[{"comment":"Model section (overdamped Langevin equations with antisymmetric mobility matrix): the direct insertion of the odd mobility term for particles coupled to distinct heat baths requires explicit verification that the resulting Fokker-Planck operator remains consistent with the position-dependent diffusion matrix and admits a normalizable stationary density whose probability currents can be unambiguously decomposed. No microscopic derivation from an underdamped Hamiltonian or check against local detailed balance is supplied; this assumption is load-bearing for all subsequent exact-solution claims.","section":"Model definition"},{"comment":"Current decomposition and conductance calculation (results section): the claim that the handed current component enhances thermal conductance while leaving net heat current and total dissipation invariant under reversal must be shown to survive the two-temperature diffusion matrix; the abstract and reader's summary indicate the partition is performed, but the consistency of the decomposition with the antisymmetric mobility in the presence of unequal temperatures needs explicit demonstration (e.g., via the explicit form of the stationary current or entropy-production formula).","section":"Results on currents and heat transfer"}],"minor_comments":[{"comment":"Clarify the precise definition and units of the odd mobility coefficient and its relation to the symmetric mobility matrix in the two-particle system.","section":"Notation and model"},{"comment":"Add a brief statement on the range of validity of the overdamped approximation when odd mobility is present.","section":"Introduction or model"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below, clarifying the model construction and the explicit demonstrations in our exact solution. Where appropriate, we indicate revisions that will be incorporated in the revised version.","responses":[{"response":"The model is introduced phenomenologically as an overdamped Langevin system with a constant antisymmetric mobility matrix added to the standard two-temperature setup. The Fokker-Planck operator follows directly from the Langevin equations; because the mobility (and thus diffusion) matrix is position-independent and the confining potentials are harmonic, the operator is linear with constant coefficients. The stationary density is the explicit multivariate Gaussian obtained by solving the Lyapunov equation for the covariance matrix, which is always normalizable for positive temperatures. The probability currents are then constructed unambiguously from this density and the drift vector, allowing the decomposition into irreversible and handed components shown in the results. While a microscopic derivation from an underdamped Hamiltonian is not supplied, the overdamped model is internally consistent, as verified by the existence and uniqueness of the stationary solution and the well-defined currents. We will add a short paragraph and footnote in the model section confirming the FP operator structure and Gaussian stationarity.","revision_made":"partial","referee_comment":"[Model definition] Model section (overdamped Langevin equations with antisymmetric mobility matrix): the direct insertion of the odd mobility term for particles coupled to distinct heat baths requires explicit verification that the resulting Fokker-Planck operator remains consistent with the position-dependent diffusion matrix and admits a normalizable stationary density whose probability currents can be unambiguously decomposed. No microscopic derivation from an underdamped Hamiltonian or check against local detailed balance is supplied; this assumption is load-bearing for all subsequent exact-solution claims."},{"response":"The current decomposition is performed explicitly after obtaining the exact stationary covariance from the two-temperature diffusion matrix (which incorporates the unequal temperatures via the diagonal diffusion blocks). The antisymmetric mobility enters the drift, and the resulting stationary current is split into the standard irreversible part (driven by temperature difference) and the additional handed part (proportional to the odd mobility coefficient). Substituting these currents into the heat-flow and entropy-production expressions yields the stated invariance under odd-mobility reversal, because the handed contribution is odd under that reversal while the net heat current and total dissipation are even. These relations are derived analytically in the results section using the explicit covariance and current formulas. To make the consistency with the two-temperature matrix fully transparent, we will add one intermediate equation showing the stationary current vector before the decomposition.","revision_made":"partial","referee_comment":"[Results on currents and heat transfer] Current decomposition and conductance calculation (results section): the claim that the handed current component enhances thermal conductance while leaving net heat current and total dissipation invariant under reversal must be shown to survive the two-temperature diffusion matrix; the abstract and reader's summary indicate the partition is performed, but the consistency of the decomposition with the antisymmetric mobility in the presence of unequal temperatures needs explicit demonstration (e.g., via the explicit form of the stationary current or entropy-production formula)."}],"tokens_in":1393,"tokens_out":660,"duration_ms":46396,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this paper works out closed-form expressions for the steady currents, heat flows, and entropy production in a minimal dimer where two particles sit at different temperatures, are spring-coupled, and have an added odd mobility term. The handed correlations between particles and the boost in thermal conductance appear only from the joint action of the three ingredients, and both the net heat current and total dissipation stay unchanged when the odd response is reversed.\n\nWhat the paper does cleanly is split the probability current into the usual irreversible part from the temperature difference and an extra handed part generated by the odd term. When viewed per particle this handed part becomes a pair of counter-rotating circulations inside the traps. Having everything solvable exactly is useful for a controlled example that links odd transport to heat exchange without torques or spatial asymmetry.\n\nThe soft spot is the starting modeling step. The odd mobility is written directly into the overdamped Langevin equations as an antisymmetric addition to the mobility matrix. With different temperatures the diffusion matrix is no longer uniform, and it is not automatic that the resulting Fokker-Planck operator stays consistent or that the currents can be cleanly partitioned without extra constraints. The abstract presents the results as following from the equations, but the lack of a microscopic derivation or explicit consistency check for the two-temperature case is the part that needs scrutiny.\n\nThis is for people working on odd transport and minimal nonequilibrium models in soft matter. A reader who wants concrete analytical expressions to compare against simulations or other setups would get value from it. The work is coherent on its own terms and the exact solvability makes the claims testable, so it deserves a serious referee even if the odd-term assumption draws the most questions.","headline":"Exact solution of the odd-mobility two-temperature dimer shows handed correlations and conductance enhancement that require all three ingredients and survive odd reversal.","tokens_in":2406,"tokens_out":415,"would_cite":false,"duration_ms":62294,"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":"Odd mobility in a two-temperature Brownian dimer generates handed correlations between the particles and increases thermal conductance while leaving net heat current unchanged under reversal.","keywords":["odd mobility","Brownian dimer","two-temperature system","handed correlations","thermal conductance","probability currents","nonequilibrium dynamics","Langevin equations"],"falsifier":"Compute the cross-correlation functions of the two particle positions and check whether a nonzero antisymmetric (handed) component appears precisely when the odd mobility coefficient is nonzero, and whether reversing its sign increases measured conductance while leaving net heat flow unchanged.","tokens_in":2624,"feed_emoji":"🌀","tokens_out":748,"duration_ms":50855,"temperature":0.7,"pith_summary":"The paper studies two harmonically coupled particles, each coupled to a different temperature reservoir, with an added odd mobility term in their overdamped dynamics. This antisymmetric term converts the conservative spring forces into transverse motion and produces additional circulating probability currents. The exact analytic solution shows that handed correlations between the two particles appear only when temperature imbalance, elastic coupling, and odd mobility are all present, while each particle's marginal distribution stays isotropic. These correlations reverse with the sign of the odd mobility, and the same reversal increases the thermal conductance between the reservoirs without altering the net heat current or the total dissipation.","feed_headline":"Odd mobility creates handed correlations in two-temperature dimer","feed_subtitle":"Exact solution shows boosted conductance between reservoirs while net heat current and dissipation stay unchanged on reversal.","key_machinery":"The odd mobility term, an antisymmetric addition to the mobility matrix in the overdamped Langevin equations that converts conservative forces into transverse velocity components.","core_discovery":"Our exact solution shows that odd mobility creates handed correlations between the two particles while leaving the individual particle distributions isotropic. These correlations arise only when temperature imbalance, elastic coupling, and odd mobility act together, and their handedness reverses when the odd response is reversed. The steady probability current contains two distinct parts: the ordinary irreversible current of a two-temperature dimer and an additional handed contribution generated by odd mobility. When projected onto the motion of each particle, this handed contribution becomes a pair of counter-rotating circulating currents inside the traps. We show that odd mobility enhances","pith_inferences":["The same odd-mobility mechanism could be implemented in colloidal experiments via position-dependent feedback forces to test the predicted chiral currents.","The selective boost in conductance without net-flow asymmetry suggests a route to directional heat control in microscopic systems that avoids explicit breaking of time-reversal symmetry in the driving.","The separation of the probability current into ordinary and handed parts may generalize to larger particle networks or active-matter models where antisymmetric transport coefficients appear."],"forward_implications":["Handed correlations between the particles exist only when temperature difference, spring coupling, and odd mobility are simultaneously present.","The steady-state probability current acquires an extra handed component on top of the usual irreversible flow of the two-temperature dimer.","Thermal conductance between the two reservoirs increases with the magnitude of the odd mobility.","Reversing the sign of the odd mobility reverses the handedness of correlations and currents but leaves the net heat current and total dissipation invariant."],"fun_headline_variants":["Odd mobility produces handed correlations in two-temperature dimer","Handed correlations arise in two-temperature dimer with odd mobility","Odd mobility links heat exchange to circulating currents in dimer","Counter-rotating currents inside traps from odd mobility in dimer"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"An odd mobility term with antisymmetric coefficients can be inserted directly into the overdamped Langevin equations without requiring a microscopic Hamiltonian derivation or further consistency constraints.","fun_headline_variants_meta":{"raw":{"variants":["Odd mobility produces handed correlations in two-temperature dimer","Handed correlations arise in two-temperature dimer with odd mobility","Odd mobility links heat exchange to circulating currents in dimer","Counter-rotating currents inside traps from odd mobility in dimer"]},"model":"grok-4.3","cost_usd":0.007806,"raw_usage":{"total_tokens":3569,"prompt_tokens":678,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":78062000,"prompt_tokens_details":{"text_tokens":678,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2829,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":678,"tokens_out":62,"duration_ms":46128,"temperature":1.0,"reasoning_tokens":2829,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T02:45:59.028876+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Compute the cross-correlation functions of the two particle positions and check whether a nonzero antisymmetric (handed) component appears precisely when the odd mobility coefficient is nonzero, and whether reversing its sign increases measured conductance while leaving net heat flow unchanged.","supporting_citations":[],"review_version":1}