{"id":"f7dbf055-22a8-4c12-bc98-faee09ee385b","arxiv_id":"2412.20689","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In the adiabatic limit, a symmetric passive disk in a chiral active bath obeys an odd Einstein relation D⊥ = T_eff μ⊥, while rods and wedges show increasingly irreversible dynamics.","lead":"A passive object floating in a swirling active fluid picks up odd transport properties, like moving sideways or spinning, that depend on its shape. This paper builds a general theory for such chiral ratchets and shows a surprising Einstein-style link between two odd transport coefficients in the heavy-object limit.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Adiabatic limit may not hold at the masses simulated for rod and wedge, so the reported ratchet velocities and two-temperature ratios may carry uncontrolled finite-mass corrections.","rationale":"The reader identified the adiabatic factorization as the weakest assumption, and I agree. The paper's own narrative depends on taking the adiabatic limit seriously: the disk's effective equilibrium (Eq. 8), the odd Einstein relation (Eq. 9), the persistent momentum-space currents (Eq. 10), the rod's two temperatures (Eq. 12), and the wedge's full irreversibility are all presented as adiabatic-limit results. The disk is tested over a wide mass range, but the rod and wedge—the species that carry the headline 'increasingly irreversible' claim—are only shown at a single mass where ε is not unambiguously small. This is not an internal inconsistency in the derivation, but a gap in the evidence that the observed behaviors belong to the asymptotic regime rather than to crossover physics. The paper also acknowledges neglecting long-time tails, which may further perturb the quantitative values at finite mass. The concrete test I propose directly measures whether finite-mass corrections are under control. Since the reader already conditioned the verdict on the deferred derivations and missing data, my assessment does not change the verdict: the paper remains a well-motivated and credible contribution whose central quantitative claims await this additional verification.","tokens_in":9725,"tokens_out":2605,"duration_ms":27662,"concrete_test":"Run the rod and wedge simulations at M = 10^3 and 10^4 (ε ≈ 0.1 and 0.032) with all other parameters fixed (ℓp = 10, ℓg = 5, rod/wedge geometry as in Figs. 3–4). If the ratchet velocities v⊥ and Ω, and the temperature ratio T_R^eff/T_Θ^eff, shift by more than ~10% relative to the M = 100 values, the published results are not adiabatic-limit quantities and the central claims require reinterpretation. A second, complementary check is to plot these observables against ε and verify a well-defined ε→0 extrapolation consistent with the reported values.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central arguments—the odd Einstein relation for the disk, the two-temperature description of the rod, and the fully irreversible wedge dynamics—are derived in the adiabatic limit defined by ε = sqrt(γ/(D_r M)) << 1 (paragraph before Eq. (3)). The disk's convergence is demonstrated with a systematic mass sweep (M ∈ [10^−2, 10^3], Fig. 2), but the rod and wedge results are shown at M = 100 only (Figs. 3 and 4). With the stated parameters (γ = 1, f0 = 1, ℓp = 10 ⇒ D_r = 0.1), ε = sqrt(10/M). At M = 100, ε ≈ 0.316, which is not small compared to 1; even at M = 10^3, ε ≈ 0.1. The paper claims 'large object mass' but does not demonstrate that the rod and wedge observables—v⊥, Ω, T_R^eff/T_Θ^eff—have converged to their adiabatic limits. If finite-mass corrections are significant, the identification of 'increasing irreversibility with decreasing symmetry' as a property of the adiabatic limit would be confounded with mass-dependent effects. The deferred derivations in the companion paper [42] do not provide the missing mass-scaling evidence. This is the single most load-bearing concern because it sits directly beneath Eqs. (9), (10), and (12) and the ratchet predictions of Fig. 4.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Langevin description for a passive rigid body of arbitrary shape immersed in a chiral active bath, in the adiabatic limit of large object mass. It predicts that a disk has an effective equilibrium description with an Einstein relation for both even and odd transport coefficients, a rod has two distinct effective temperatures, and a wedge is fully irreversible with both rotational and translational ratchet motion. The paper also derives a multipole expansion for the far-field density and current of the bath and verifies it numerically. The claims are supported by molecular dynamics simulations for a disk, rod, and wedge, with the disk showing detailed mass-dependence.","tokens_in":10020,"tokens_out":5861,"duration_ms":54128,"significance":"If the results hold, they unify and extend odd transport phenomena in chiral active baths, and the symmetry hierarchy (disk to rod to wedge) is an elegant organizing principle. The disk Einstein relation for odd coefficients is a nontrivial prediction, and the far-field multipole formulas are practical tools. A notable strength is that the simulations are made reproducible with public code, and the disk mass sweep provides a stringent test of the adiabatic limit. However, the central analytic derivations are deferred to an unpublished companion, and the rod/wedge simulations are only at one mass that may not be in the adiabatic regime; these gaps must be addressed before the full scope of the claims is established.","major_comments":[{"comment":"The adiabatic parameter is defined in the paragraph before Eq. (3) as ε = sqrt(γ/(D_r M)). With the stated parameters f0 = γ = 1 and ℓp = 10, one has D_r = 0.1, so at M = 100, ε ≈ 0.316, which is not small. The disk results are shown to converge to the adiabatic limit via a mass sweep over M ∈ [10^-2, 10^3] (Fig. 2), but the rod (Fig. 3) and wedge (Fig. 4) results are presented only at M = 100. Without a mass sweep for these shapes, the two-temperature description of Eq. (12) and the ratchet velocities v⊥ and Ω in Fig. 4a cannot be confirmed as adiabatic-limit results; they may carry significant finite-mass corrections that could alter the claimed symmetry hierarchy. Please provide mass sweeps for the rod and wedge, or otherwise quantify the size of O(ε) corrections at M = 100.","section":"Paragraph before Eq. (3); Figs. 3 and 4"},{"comment":"The effective Langevin dynamics (3), the Agarwal formula (4), and the Green-Kubo relation (6) are stated without derivation, as are the Einstein relations (9) and the inequality (10). These are deferred to a companion paper [42] that is listed as \"submitted to phys. rev. e\" and is not accessible. Since these equations are the foundation for all subsequent claims, the Letter is not self-contained. At minimum, the companion should be made available (e.g., on arXiv) or the key steps of the derivation should be included in an appendix or supplementary material.","section":"Eqs. (3)-(6) and (9)-(10); reference [42]"},{"comment":"The claim that the adiabatic dynamics of rotationally-symmetric objects is statistically reversible under combined time reversal and chirality inversion is presented as the rationalization for the effective equilibrium of the disk and the two-temperature description of the rod, but no argument is given in the Letter beyond a citation to [42]. Since this hidden symmetry is a load-bearing concept for the central hierarchy, please include a concise derivation or explicit statement of the symmetry argument in the Letter.","section":"Section 'The C2 spinning rod'; reference [42]"}],"minor_comments":[{"comment":"The heading reads \"F ar-field density and currents\"; this should be \"Far-field density and currents\".","section":"Fig. 5 heading"},{"comment":"The phrase \"acts over a vanishing small distance\" should be \"acts over a vanishingly small distance\".","section":"Section 'The Π steering wedge'"},{"comment":"The companion paper is cited as \"submitted to phys. rev. e\"; please update the reference with an arXiv identifier or a published DOI when available, as the current form prevents readers from accessing the derivations.","section":"Reference [42]"},{"comment":"The notation Db∥ is used in Eq. (13) but the decomposition of the bath diffusivity into even and odd parts is not defined in the main text; please clarify that Db∥ is the isotropic part of the bath diffusivity.","section":"Eq. (13)"}],"recommendation":"major_revision","confidential_remarks":"The paper's central claims are plausible and the disk results are convincing, but the reliance on an unpublished companion for the main derivations and the absence of mass sweeps for the rod and wedge are significant concerns. The journal may wish to require that the companion be made available before publication, and that the authors provide a more thorough check of the adiabatic limit for all object shapes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a nice paper with a real idea, and the disk results look solid. The rod and wedge part, which is the advertised symmetry hierarchy, is on shakier ground than the authors acknowledge, because the simulations are done at a mass where the adiabatic parameter isn't that small.\n\nWhat's new: they give the most general underdamped Langevin description for a rigid body in a chiral active bath, Eqs. (3)-(6), using an Agarwal-style friction formula and Green-Kubo noise correlations. From that they derive an odd Einstein relation D⊥=T^eff μ⊥ for rotationally symmetric objects, show that odd momentum-space currents persist because λ⊥≠T^eff ζ⊥, and classify increasing irreversibility with decreasing symmetry: disk equilibrates, rod has two temperatures, wedge ratchets. The far-field multipole predictions, Eq. (14)-(17), are independently tested numerically. That's a solid package of results, and the code is public.\n\nThe soft spots, in rough order. First, the analytic derivations for the central equations are all in an unpublished companion [42]. That's a real deficiency for a Letter: the referee can't verify Eqs. (3)-(6) or (9)-(12) from the text. Second, and more specific, the adiabatic limit claim isn't checked for the rod and wedge. The paper defines ε=sqrt(γ/(D_r M)); with their parameters (γ=1, f0=1, ℓp=10), ε≈0.316 at M=100. That's not very small. They show a systematic mass sweep for the disk, but the rod and wedge are only shown at M=100 (Figs. 3 and 4). So the observed two-temperature behavior and wedge ratchet velocities might have finite-mass corrections, and the statement that 'the dynamics becomes increasingly irreversible' as symmetry decreases could be partly a mass effect. The paper says 'large object mass' but never demonstrates convergence for those shapes. The stress-test note lands.\n\nThere are also minor issues: limited error bars on the temperature ratio and ratchet velocities, and the claim that T_R^eff is 'nearly twice as hot' needs a robust estimate.\n\nOverall: the central framework is credible and the disk results are well supported. I'd send this to peer review, but the referee should ask for (i) mass sweeps for rod and wedge showing convergence of Ω, v⊥, and the temperature ratio, (ii) full derivations either in an appendix or a publicly available companion, and (iii) error bars. The paper is worth the effort; it's just not ready as is.","headline":"A genuinely interesting framework for odd transport in chiral baths, but the advertised disk-rod-wedge hierarchy needs a mass sweep before the adiabatic claim holds.","tokens_in":10539,"tokens_out":3176,"would_cite":true,"duration_ms":32152,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For heavy symmetric disks in chiral baths, odd diffusion and odd mobility obey an Einstein relation, so odd positional currents vanish while odd momentum-space currents persist.","keywords":["chiral active bath","odd diffusivity","odd mobility","Einstein relation","ratchet motion","adiabatic elimination","effective temperature","far-field multipole expansion"],"falsifier":"In a molecular dynamics simulation of a harmonically confined disk in a chiral active bath at $\\epsilon = \\sqrt{\\gamma/(D_r M)} \\ll 1$, measure the steady-state position flux $\\mathbf{J}_R^{ss} = (T^{\\mathrm{eff}}\\boldsymbol{\\mu} - \\mathbf{D})\\nabla\\rho_R$ and the ratio $D_\\perp/\\mu_\\perp$. If $\\mathbf{J}_R^{ss}$ does not vanish or $D_\\perp/\\mu_\\perp \\neq T^{\\mathrm{eff}}$ within statistical error, the paper's odd Einstein relation is not correct.","tokens_in":9538,"feed_emoji":"🔄","tokens_out":7645,"duration_ms":75044,"temperature":0.7,"pith_summary":"This paper answers how a passive object's shape controls the nonequilibrium dynamics it inherits from a chiral active bath: at large object mass, the bath can be adiabatically eliminated, and the paper derives exact effective Langevin dynamics. Its central result is that for a rotationally symmetric disk the odd diffusion and odd mobility satisfy an Einstein relation; consequently positional-space odd currents vanish, even though momentum-space odd currents persist because the odd noise and friction coefficients do not satisfy a second fluctuation-dissipation relation. As symmetry is lowered, equilibrium-like behaviour degrades: a rod displays two different effective temperatures, and a wedge acts as a full ratchet. The paper also derives the universal far-field density and current patterns in the bath, measured in simulations, and shows they carry the same broken symmetries. A sympathetic reader would care because this gives a first-principles framework for using object shape and mass to engineer ratchet and odd transport in chiral active fluids.","feed_headline":"Heavy disks in chiral baths obey an odd Einstein relation","feed_subtitle":"At large object mass, position-space odd currents vanish while momentum-space currents persist.","key_machinery":"The central object is the adiabatically reduced Langevin description, where the object evolves under mean bath forces and torques, a $2\\times2$ block friction matrix $\\zeta$ built from bath-force correlations via a Green-Kubo-type formula, and Gaussian noise whose correlation matrix $\\lambda$ obeys another Green-Kubo formula. The argument is carried by the symmetry structure of these matrices: isotropy for the disk, $C_2$ symmetry for the rod (which decouples translation from rotation), and full breaking of $C_n$ symmetry for the wedge (which couples them). The odd components of these matrices, coming from the chirality of the bath, are what generate odd diffusivity, odd mobility, ratchet torques, and the persistent momentum-space currents.","core_discovery":"In the adiabatic limit of a massive object, the paper derives the most general Langevin dynamics for a rigid body in a chiral active bath by integrating out the bath degrees of freedom, leaving effective friction, noise, mean force, and mean torque coefficients. For a rotationally symmetric disk, it shows that the even and odd parts of diffusivity and mobility are connected by $D_\\parallel = T^{\\mathrm{eff}}\\mu_\\parallel$ and $D_\\perp = T^{\\mathrm{eff}}\\mu_\\perp$, so the two odd contributions to the steady-state position-space flux exactly cancel and the disk adopts a Boltzmann distribution with a single effective temperature $T^{\\mathrm{eff}}$. However, the corresponding noise and friction coefficients satisfy $\\lambda_\\parallel = T^{\\mathrm{eff}}\\zeta_\\parallel$ but $\\lambda_\\perp \\neq T^{\\mathrm{eff}}\\zeta_\\perp$, leaving persistent circulating currents in momentum space as a unique odd signature of the chiral nonequilibrium bath. For a $C_2$-symmetric rod, translational and rotational dynamics decouple, producing a net rotational ratchet velocity and two independent effective temperatures, one translational and one rotational. For a wedge with no $C_n$ symmetry, rotation and translation couple in both friction and noise, so no effective temperatures exist and the wedge behaves as both a translational and rotational ratchet; the broken symmetry is also imprinted on the bath as universal far-field density modulations and currents with dipolar and quadrupolar structure.","pith_inferences":["A testable extension not in the paper: the ratio $D_\\perp/\\mu_\\perp$ for a heavy symmetric probe in a real chiral active suspension could be used as a direct thermometer of $T^{\\mathrm{eff}}$, and deviations from $D_\\parallel/\\mu_\\parallel$ would indicate departure from the adiabatic limit.","The far-field dipole/quadrupole density fields imply long-ranged bath-mediated interactions between two objects; since a rod's or wedge's dipole moment has a sign and orientation fixed by its chirality, pairs should experience chiral-selective attraction or repulsion—an effect the paper does not compute.","For non-symmetric objects where scalar effective temperatures fail, one could define a matrix-valued effective temperature $\\mathbf{T} = \\lambda \\zeta^{-1}$; for the wedge this matrix would be non-symmetric, and its antisymmetric part would quantify the failure of any equilibrium-like description."],"forward_implications":["A heavy disk confined in a chiral active bath has Boltzmann positional statistics with a single effective temperature $T^{\\mathrm{eff}}$, so its steady-state position-space flux vanishes even though the bath is out of equilibrium.","For a rod, translational and rotational degrees of freedom independently equilibrate at two temperatures $T_R^{\\mathrm{eff}}$ and $T_\\Theta^{\\mathrm{eff}}$, and in the adiabatic limit the rod spins at the same angular velocity whether pinned or free to translate.","A wedge loses any effective equilibrium description; it translates and rotates as a ratchet, with the perpendicular ratchet speed and angular velocity peaked when the gyroradius $\\ell_g$ matches the wedge size, and the parallel velocity can reverse sign with $\\ell_g$.","The bath develops universal far-field density modulations and currents: a rod produces a quadrupolar leading field, a wedge a dipolar one, and bath chirality rotates these patterns; the rotational near-field flux is tied to the torque on the object.","Odd transport coefficients of a disk are maximised when the disk diameter is of order $\\ell_g$, giving a design rule for maximal odd response, and outside the adiabatic limit the disk's odd Einstein relation breaks down with circulating position-space currents reappearing."],"supporting_citations":[{"why":"Adiabatic effective-equilibrium description of a passive object in an active bath, which the paper generalises to chiral baths.","marker":"[17]"},{"why":"Introduces odd diffusivity for chiral active baths, which the disk's $D_\\perp$ is measured against.","marker":"[32]"},{"why":"Gives odd mobility in chiral active matter, the coefficient interpreted as $\\mu_\\perp = (\\zeta^{-1})_\\perp$ here.","marker":"[34]"},{"why":"Provides the odd-mobility theory used to connect the disk's pulling response to $\\mu_\\perp$.","marker":"[35]"},{"why":"Underlying adiabatic elimination of fast bath variables used to derive the object Langevin equation.","marker":"[43]"},{"why":"Supplies the Green-Kubo-type formula used to compute the friction matrix $\\zeta$ from bath-force correlations.","marker":"[46]"},{"why":"Far-field multipole method for a passive object in an active bath that is extended to chirality in deriving the density and current fields.","marker":"[64]"}],"fun_headline_variants":["Heavy disks in chiral baths: odd diffusion meets odd mobility","Odd Einstein relation ties diffusion and mobility in chiral baths","Chiral baths: heavy disks obey an odd Einstein relation","Symmetry dictates irreversibility in chiral active baths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the bath reaches a quasi-static conditional steady state around each instantaneous object configuration before the object moves appreciably—the factorisation $\\rho \\approx \\rho_o \\rho_b$ with $\\epsilon = \\sqrt{\\gamma/(D_r M)} \\ll 1$—together with the neglect of long-time tails from conservation laws.","fun_headline_variants_meta":{"raw":{"variants":["Heavy disks in chiral baths: odd diffusion meets odd mobility","Odd Einstein relation ties diffusion and mobility in chiral baths","Chiral baths: heavy disks obey an odd Einstein relation","Symmetry dictates irreversibility in chiral active baths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000831,"raw_usage":{"total_tokens":3633,"prompt_tokens":956,"completion_tokens":2677,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":2620}},"tokens_in":572,"tokens_out":2677,"duration_ms":20518,"temperature":1.0,"reasoning_tokens":2620,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:14:35.122956+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a molecular dynamics simulation of a harmonically confined disk in a chiral active bath at $\\epsilon = \\sqrt{\\gamma/(D_r M)} \\ll 1$, measure the steady-state position flux $\\mathbf{J}_R^{ss} = (T^{\\mathrm{eff}}\\boldsymbol{\\mu} - \\mathbf{D})\\nabla\\rho_R$ and the ratio $D_\\perp/\\mu_\\perp$. If $\\mathbf{J}_R^{ss}$ does not vanish or $D_\\perp/\\mu_\\perp \\neq T^{\\mathrm{eff}}$ within statistical error, the paper's odd Einstein relation is not correct.","supporting_citations":[{"cited_title":"Active Microrheology, Hall Effect, and Jamming in Chiral Fluids","cited_arxiv_id":"1901.11107","evidence_quote":"Gives odd mobility in chiral active matter, the coefficient interpreted as $\\mu_\\perp = (\\zeta^{-1})_\\perp$ here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the odd-mobility theory used to connect the disk's pulling response to $\\mu_\\perp$."},{"cited_title":"Van Kampen and I","cited_arxiv_id":null,"evidence_quote":"Underlying adiabatic elimination of fast bath variables used to derive the object Langevin equation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Green-Kubo-type formula used to compute the friction matrix $\\zeta$ from bath-force correlations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Far-field multipole method for a passive object in an active bath that is extended to chirality in deriving the density and current fields."}],"review_version":1}