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REVIEW 4 major objections 3 minor 220 references

Kinetic and Hydrodynamic Theories of Chiral Intruder Dynamics in Nonequilibrium Baths

T0 review · 4 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The paper claims that chiral intruder dynamics in a nonequilibrium bath can be reduced, in the dilute limit, to a Langevin equation with explicit surface-integral coefficients, and in the dense limit to torque-density-driven edge currents t

desk verdict Serious analytic paper with genuinely new explicit results in both dilute and dense regimes; the main caveat is the load-bearing and acknowledged uncorrelated-collision assumption, but it deserves peer review. read the letter →

arxiv 2607.23223 v1 pith:YQXJG4GQ submitted 2026-07-25 cond-mat.stat-mech cond-mat.softphysics.flu-dyn

Raphaël Maire , Ignacio Pagonabarraga This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.softphysics.flu-dyn
keywords chiralactivematteroddresponseLangevinequationBoltzmann-Lorentzkinetictheoryedgecurrentstorquedensitynonequilibriumbathintruderdynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to establish a quantitative, mechanism-resolving theory of how a chiral intruder moves through an out-of-equilibrium bath, where chirality can reside in the intruder's shape, in the bath itself, or in their interaction. In the dilute regime it derives a Langevin equation whose force, damping, and noise coefficients are all given by surface integrals, cleanly separating shape chirality (which produces ratchet torques) from chiral collisions (which produce odd response and torque). In the dense regime it argues that the governing mechanism switches to torque-density-driven edge currents, which create lift forces and curvature-induced torques that a dilute kinetic theory cannot capture. The authors flag the boundary of this picture: uncorrelated collisions make shape chirality invisible to odd damping, and their companion simulations reveal a small correlation-induced odd response that the dilute theory misses by construction. If correct, the two complementary descriptions convert a symmetry taxonomy of possible chiral effects into concrete, testable formulas across densities.

What carries the argument

The central object is the generalized force-damping-noise triple (F, Γ, D) expressed as boundary integrals over the intruder's surface, together with the split into normal (α) and chiral tangential-kick (Δ) sectors. The kinetic derivation relies on a van Kampen expansion (small bath-mass expansion) of the Kramers-Moyal moments, which identifies the ratchet force as a fluctuation-driven term ∝ T_b − T_I and justifies the Gaussian Fokker-Planck closure. The geometric moments that decide which coefficients survive are perimeter P, signed area A, Q_ab = ∮ ds n̂_a n̂_b, and H_φ = ∮ ds κ_n³. In the dense regime, the machinery is the chiral Navier-Stokes equation with a torque-density term τ0 actin

What would settle it

Measure the off-diagonal translational damping of a chiral-shaped intruder (e.g., a chiral wheel) in a dilute, achiral, nonequilibrium bath with no tangential kick (Δ=0). The dilute theory predicts Γ_xy − Γ_yx = 0 identically and spontaneous rotation with torque ∝ (T_b − T_I)H_φ; a non-zero odd damping at the same low density would falsify the uncorrelated-collision premise, while a zero result would support the two-sector separation. Alternatively, reverse the sign of bath chirality in a dense chiral fluid and check that the lift force on a translating cylinder reverses proportionally to τ0.

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Extended reading notes

Core claim

The central claim is that a single intruder in a nonequilibrium bath has two complementary descriptions whose coefficients are computed, not fitted. In the dilute regime, starting from a Boltzmann-Lorentz master equation for uncorrelated binary collisions and a prescribed bath velocity distribution, a van Kampen expansion in the bath-to-intruder mass ratio produces a closed linear Langevin equation M·U̇ = F − Γ·U + √D·ζ (Eq. 60), with F, Γ, and D given explicitly by boundary integrals (Eqs. 61–63). Splitting the collision rule into a normal/dissipative sector (restitution α) and a chiral tangential-kick sector (Δ) separates the physics: shape chirality plus a nonequilibrium bath yields a rat

Load-bearing premise

The load-bearing premise is that, in the dilute regime, every intruder–bath collision is independent and the bath velocity distribution f(v) is unaffected by the intruder (Boltzmann-Lorentz assumption, Sec. II.A); the paper itself states that its companion molecular-dynamics simulations find a small but finite odd response caused by correlations, so if these correlations cannot be neglected the clean separation between shape-driven ratchet torque, collision-driven odd respons

Editorial extensions

If this is right

  • A chiral-shaped intruder in a dilute, nonequilibrium but achiral bath should spontaneously rotate with torque ∝ (T_b − T_I)H_φ; for an achiral shape in a bath with chiral collisions, rotation is instead driven by the area and Δ.
  • Odd translational damping in the dilute regime comes only from chiral intruder–bath collisions (Γ^Δ_ab ∝ P ε_ab), not from shape chirality; the paper predicts zero odd damping for a shape-chiral object in an achiral bath at this order, a direct consequence of uncorrelated collisions.
  • Sector-wise fluctuation-dissipation-like relations hold at leading order (D^α = 2T_I Γ^α and D^Δ = 2(1+α)T_b Γ^{Δ,S}), but the higher-order equilibrium fluctuation relations fail once non-Gaussian noise is retained, so no single effective temperature describes the intruder beyond leading order.
  • In a dense chiral bath, a translating circular intruder experiences a lift force perpendicular to its velocity with Γ_xy ∝ τ0, independent of the Oseen logarithmic factor, so the antisymmetric response survives the Stokes paradox.
  • A weakly non-circular intruder in a dense chiral bath experiences curvature-induced torque F_φ = π ε² τ0 R0² (m²−1)(m−2), leading to a steady angular velocity Ω = τ0(m−2)/(2ηm) that is independent of deformation amplitude at leading order.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the dilute prediction of zero shape-induced odd damping is generic, then observing a finite Γ_xy at low densities in an achiral nonequilibrium bath gives a direct quantitative measure of intruder–bath correlations—a diagnostic that pure symmetry arguments cannot supply.
  • The dense-regime formula suggests a design rule for chiral rotation or sorting: any smooth object with curvature variation placed in a bath with nonzero torque density τ0 should rotate even with perfect-slip surfaces, and the torque is maximized by tuning the symmetry index m of the shape.
  • The two regimes imply a crossover in the origin of odd response—collision-driven at low density (∝ Δ) and edge-current/inertia-driven at high density (∝ τ0); measuring the sign and magnitude of Γ_xy as a function of bath density would test the proposed unified two-scale picture.
  • The breakdown of the fluctuation-dissipation hierarchy at higher order implies that the third cumulant of intruder velocity fluctuations should show signatures of the discarded non-Gaussian noise C_ijk even when the second cumulant is well described by an effective temperature.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper develops two complementary frameworks for a chiral intruder in a nonequilibrium bath. In the dilute regime, starting from a Boltzmann–Lorentz master equation and a van Kampen expansion in the bath-to-intruder mass ratio, it derives a linear Langevin equation whose damping, noise, and ratchet force/torque coefficients are given by explicit boundary integrals over the intruder shape. This is used to separate shape chirality (ratchet torque, no translational odd damping) from interaction chirality (odd damping, torque). In the dense regime, the bath is described by a chiral Navier–Stokes equation with a torque density that produces edge currents; the paper claims these currents generate an Oseen-type lift force and a curvature-induced torque. It also derives formal linear-response integral formulas for the damping matrix and shows that various fluctuation-dissipation-like relations hold only at leading order.

Significance. If the central claims hold, the paper would provide a useful, analytically explicit bridge between kinetic and hydrodynamic descriptions of chiral intruders, with concrete geometric formulas and a physical mechanism (torque-density edge currents) that is distinct from odd viscosity. The paper is unusually transparent about its approximations, including the uncontrolled truncation in the dilute theory and the discrepancy between its zero-odd-damping prediction and reported companion simulations. The explicit formulas for the damping matrix, the ratchet torque, and the Oseen lift force are potentially valuable for future experimental and numerical work. However, several load-bearing coefficients contain internal inconsistencies or rely on assumptions whose quantitative error is not assessed, so the current version is not yet a reliable reference for these predictions.

major comments (4)
  1. [Sec. II.C.2, Eqs. (52), (61)] The intruder temperature is defined as T_I = K3/(2K1)(1+α)^2 T_b, and the text immediately states that at equilibrium α=1 with a Gaussian bath (K3/(2K1)=1) one has T_I=T_b. With the displayed formula, however, T_I=4T_b. This inconsistent factor propagates into the ratchet force F_i^(α) ∝ (T_b−T_I) and into the fluctuation-dissipation relation D^(α)=2T_I Γ^(α). The correct prefactor appears to be (1+α)/2 (or (1+α)^2/4), not (1+α)^2. All temperature-dependent coefficients in Sec. III and Appendix E must be re-derived before the quantitative claims can be accepted.
  2. [Sec. II.C.1 and II.D] The derivation keeps the quadratic drift N_ijk while dropping E_ijk and C_ijk, which enter at the same order in the van Kampen expansion; the text calls this a standard approximation rather than a controlled truncation. The subsequent replacement of N_ijk U_j U_k by N_ijk S_lin_jk is a mean-field closure. Since the ratchet force in Eq. (57) is generated by this closure at a nominal order where a discarded term is equally important, the explicit coefficient of F_i is not a systematically derived result. The paper should provide a diagnostic—for example, the magnitude of the C_ijk contribution in a solvable limit, or a direct numerical estimate of the error in F_i—or clearly state that the ratchet coefficient is model-dependent at the same order as the neglected terms.
  3. [Sec. IV, Table I] One of the headline dilute results is the vanishing odd translational damping for a chiral intruder in an achiral nonequilibrium bath. The paper acknowledges in Sec. IV that companion MD simulations find a small but finite odd response generated by bath–intruder correlations. Because this vanishing coefficient is a central separation principle, the statement is only valid in the strict uncorrelated-collision limit. The authors should either provide a density-scaling estimate for the correction (e.g., whether it vanishes linearly with n_b) or explicitly reformulate the claim as a property of the Boltzmann–Lorentz model rather than a prediction for the dilute regime. Without such quantification, the clean two-mechanism picture remains a modeling outcome, not an established physical separation.
  4. [Sec. VII.D, Eq. (134)] With the sign conventions in Eqs. (82)–(83), a positive torque density τ0 produces a clockwise edge current uθ=−τ0R0^2/(2ηr). Using the displayed fields (122)–(127) in the boundary integral (128)–(131) gives Fφ = −π ε^2 τ0 R0^2 (m^2−1)(m−2), the opposite sign of Eq. (134). Consequently, Eq. (146) predicts a steady rotation counterclockwise to the edge current. If the authors use an opposite sign convention for Fφ, it should be stated; as written, the direction of the curvature-induced torque is inconsistent with the direction of the edge flow, and the sign of both the torque and the resulting angular velocity needs to be corrected or explicitly justified.
minor comments (3)
  1. [Sec. VII.A, Eqs. (109), (118)–(119)] The boundary perturbation contains a dimensional typo: for R(θ)=R0[1+εh(θ)], the normal is n = e_r − ε h'(θ) e_θ, not e_r − ε h'(θ)/R0 e_θ. The printed expansion appears to omit an R0 factor in the normal and boundary-condition terms. The final formulas for u_r and p suggest the authors used the correct expression downstream, but the displayed equations should be fixed.
  2. [Sec. II.B.3, Eq. (33)] The normalization of ψ(c) is not specified. Since the value of K3/(2K1) is used to set T_I and the text claims a value of 1 for a Gaussian bath, the definition of ψ in terms of the one-dimensional normal-velocity distribution should be written explicitly, including prefactors, to prevent a factor-of-two ambiguity.
  3. [General] The companion Letter [135] is cited for validation and for the MD observation of the small odd response, but the simulations are not available to the reader. The paper should include at least a brief statement of the simulation parameters and the measured odd-response magnitude, or state that the validation data are provided in the companion Letter and cannot be assessed independently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dilute Langevin coefficients are computed explicitly from a stated collision rule, the dense results are new calculations from a cited (self-authored) hydrodynamic framework, and the acknowledged correlation-induced limitation is stated transparently.

full rationale

The dilute derivation is self-contained: the authors state a collision rule (Eqs. 8–10) and a Boltzmann-Lorentz kernel (Eqs. 11–12), then compute Kramers–Moyal moments and organize them by a van Kampen small-mass expansion. The resulting Langevin coefficients (Eqs. 61–63) are explicit boundary integrals over shape-dependent vectors and bath velocity moments; no coefficient is fitted to the predicted odd response, ratchet torque, or damping. The vanishing of odd translational damping in the (α) sector follows algebraically from the symmetry of Q_ab (Sec. III / Appendix C), and the paper explicitly attributes any finite simulated odd response to correlations absent from the assumed kernel (Sec. IV). This is a clearly stated limitation of the model, not a circular definition of the result. In the dense regime, the chiral Navier–Stokes description is imported from Ref. 34, which shares an author with this paper, but that is a proper citation of a separate kinetic-theory derivation; the intruder-specific Oseen lift force (Eq. 107) and curvature-induced torque (Eq. 134) are new calculations from that framework, not reductions to their own outputs. The companion Letter [135] is cited for MD validation and for empirical limitations, not as a premise of the analytic derivation. I therefore find no step where a prediction is equivalent by construction to an input.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new particles or fields; its inputs are collision-rule parameters (α, Δ), a bath velocity distribution, and a torque density τ0 imported from prior kinetic theory. The main modeling choices are the ad hoc chiral collision rule and the perfect-slip boundary condition, both acknowledged.

free parameters (3)
  • Δ (bath-intruder chiral tangential kick) = not fitted; model parameter
    Introduced in Eq. (9) as the chiral sector of the collision rule; the paper states the rule is not unique. All dilute-regime chiral effects (odd Γ, torque, D_Δ) are proportional to Δ, so the theory is conditional on this modeling choice.
  • α (normal restitution coefficient) = not fitted; model parameter
    Sets dissipation in Eq. (8); F_α and ratchet forces depend on α through T_b−T_I. Chosen by hand, not fitted to data.
  • τ0 (bulk torque density) = not fitted; taken from prior kinetic theory
    The dense-regime boundary forcing and edge currents are controlled by τ0. It is a physically motivated input from the Chapman-Enskog description of Ref. 34, not a fitted parameter here.
assumptions (6)
  • domain assumption Boltzmann-Lorentz master equation with instantaneous, binary, uncorrelated collisions
    Sec. II.A, Eqs. (11)–(12). The entire dilute derivation assumes collisions are Poissonian and the bath distribution is not perturbed by the intruder.
  • ad hoc to paper Chiral collision rule of Eq. (9): J_t = 2(a + κ_t²/I)^{-1} Δ
    The paper explicitly says the collision rule is not uniquely defined and adopts this simple form; Appendix A interprets it as a coarse-grained spinner kick, but it remains a modeling input.
  • domain assumption Small-mass van Kampen expansion and weak chiral driving mΔ² ≪ T_b
    Sec. II.D. Used to close the Fokker-Planck equation at second order and to assign a single effective intruder temperature T_I.
  • ad hoc to paper Gaussian closure: neglect E_ijk and C_ijk, average the quadratic drift using the linear covariance
    Sec. II.C.1. The authors call this 'a standard approximation rather than a controlled truncation'; it affects the ratchet force and the Fokker-Planck truncation.
  • domain assumption Perfect-slip boundary condition and constant torque density τ0 at the intruder-fluid interface
    Sec. V.B. The dense edge-current mechanism and the resultant torque/odd-drag depend on this boundary condition; α=1 and Δ=0 are also set in the dense regime.
  • domain assumption Perturbative treatment: Oseen convection for lift, but no convection in the torque calculation of Sec. VII
    Sec. VII.A and Appendix G. The torque formula Eq. (134) is first order in shape deformation ε and ignores inertial corrections and sharp-corner stress concentration, which the authors admit are substantial.

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Pith. "Pith review of Kinetic and Hydrodynamic Theories of Chiral Intruder Dynamics in Nonequilibrium Baths." pith.science (2026). https://pith.science/paper/YQXJG4GQ

@misc{pith2026260723223,
  author       = {Pith},
  title        = {Pith review of: Kinetic and Hydrodynamic Theories of Chiral Intruder Dynamics in Nonequilibrium Baths},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YQXJG4GQ}},
  note         = {Machine review of arXiv:2607.23223}
}
read the original abstract

We study the chiral dynamics of an intruder immersed in a nonequilibrium bath in two complementary limits: the dilute kinetic regime and the dense hydrodynamic regime. In the dilute limit, starting from a Boltzmann-Lorentz description, we derive an effective Langevin equation whose coefficients are given explicitly by geometry-dependent boundary integrals. This formulation separates the effects of intruder-shape chirality from those of chiral intruder-bath interactions. We find that the chiral interactions generate an odd response and a torque, whereas the chirality of the intruder leads to a ratchet effect. We also show that fluctuation-dissipation-like relations exist and that certain symmetry-allowed couplings vanish in the dilute regime. In the dense regime, we argue that intruder dynamics are governed primarily by bath hydrodynamics and torque-density-driven edge currents not captured by the previous framework. These currents can generate both an antisymmetric drag and a curvature-induced torque, leading to an antisymmetric response when inertia is accounted for. Taken together, these results provide a step toward understanding the mechanisms governing the chiral dynamics of an intruder in a nonequilibrium bath across different scales.

Figures

Figures reproduced from arXiv: 2607.23223 by the authors.

Figure 1
Figure 1. FIG. 1. Cartoon of the intruder and its parametrization [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Pressure and velocity field (streamline plot) (a, c, e) around an intruder in a chiral bath using Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Pressure and velocity fields around a [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Examples of wheels as given by Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p034_4.png]

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Reference graph

Works this paper leans on

220 extracted references · 12 linked inside Pith

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    fluctuation

    Generality In this Appendix, we clarify when the fluctuation- dissipation-like relations found in the main text hold. Since detailed balance is broken at the level of the Boltzmann-Lorentz equation, we cannot expect an equilibrium-like relation to persist at all orders in the expansionϵ. For simplicity, we focus on the case ∆ = 0. The analysis can be exte...

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    (45), ∂P ∂t =−∂ i [AiP] + 1 2 ∂i∂j [BijP]− 1 6 ∂i∂j∂k [Cijk P], (D1) where we recall that∂ i ≡∂ Πi

    Expected hierarchy at equilibrium Consider the Kramers-Moyal equation truncated at third order, Eq. (45), ∂P ∂t =−∂ i [AiP] + 1 2 ∂i∂j [BijP]− 1 6 ∂i∂j∂k [Cijk P], (D1) where we recall that∂ i ≡∂ Πi . The truncation should be understood as the neglect of higher-order terms in a van Kampen expansion. We also discarded the reversible advective current, whic...

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    Theα-sector is simple: Γ(α) ab ∝ I dsˆna ˆnb =Q ab,(C12) which is symmetric and therefore doesnotgenerate odd transport, even for a chiral intruder

    T ranslational damping:Γ ab. Theα-sector is simple: Γ(α) ab ∝ I dsˆna ˆnb =Q ab,(C12) which is symmetric and therefore doesnotgenerate odd transport, even for a chiral intruder. This differs from Ref. 133, where odd transport arises in an achiral nonequilibrium bath with a chiral intruder. As we ex- plain below, the vanishing found here follows from the a...

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    preserves the fluctuation in the force but changes the sign of the torque

    T ranslational-rotation damping:Γ aφ. The mixed blocks follow directly from the definitions: Γ(α) φa ∝ I dsκn ˆna =W a,Γ (α) aφ ∝ I dsˆnaκn =W a, (C19) so theα-sector is symmetric in the translation-rotation couplings, Γ(α) aφ = Γ(α) φa .(C20) For the ∆-sector, however, Γ(∆) φa ∝ I dsκt ˆna =S a,(C21) Γ(∆) aφ ∝ I dsκnˆta =T a =ε abWb.(C22) 28 These two ve...

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    For the rotation damping in the normal sector, we find: Γ(α) φφ ∝ I dsκ2 n =H n >0,(C37) where positivity is immediate

    Rotation damping:Γ φφ. For the rotation damping in the normal sector, we find: Γ(α) φφ ∝ I dsκ2 n =H n >0,(C37) where positivity is immediate. The chiral contribution is Γ(∆) φφ ∝ −∆ I dsκtκn =−H t∆.(C38) The scalarH t changes sign under reflection and there- fore vanishes for any achiral body. A nonzero Γ (∆) φφ thus requires a chiral shape. Once again, ...

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    In the dissipative sector, we find, D(α) ij = 2TI Γ(α) ij ,(C40) which is a fluctuation-dissipation relation for theα- sector

    Diffusion tensor:D ij The diffusion tensor is constructed from similar geo- metric objects. In the dissipative sector, we find, D(α) ij = 2TI Γ(α) ij ,(C40) which is a fluctuation-dissipation relation for theα- sector. Note, however, that the temperatureT I is not the same as that of the bathT b for a nonequilibrium dy- namics. Moreover,T I corresponds to...

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    ratchet effect

    Violation of detailed balance and the higher-order fluctuation relations in a nonequilibrium bath From the coefficients derived in the main text, we have at ∆ = 0: Ri = 1 +α 2 nbmTbϵ I dsµne(n) i ,(D9) Γij = 2(1 +α)K 1nb p mTb ϵ1/2 I dse(n) i e(n) j ,(D10) Nijk =− 1 +α 2 nbmϵ I dse(n) i e(n) j e(n) k ,(D11) Dij = (1 +α) 2K3nbTb p mTbϵ1/2 I dse(n) i e(n) j...

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    At lowest order, all fluctuation relations can still be recov- ered by introducing an effective temperature for each sec- tor [202]

    Discussion To summarize, the fluctuation-dissipation theorem de- rived in the main text for each sector ceases to hold be- yond leading order in the van Kampen expansion. At lowest order, all fluctuation relations can still be recov- ered by introducing an effective temperature for each sec- tor [202]. At higher orders, however, this description breaks do...

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    Body frame and laboratory frame We denote the body frame quantities with a tilde. For example, an intruder with a triangle shape will have on average⟨F y⟩ ≡ ⟨Flaboratory y ⟩= 0 because of isotropy, but if we always rotate the intruder to a fixed angle, then ˜Fy, the force in a...

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    If the bath particles are hard disks of diameterσ, their centers cannot approach the intruder closer than a distanceσ/2

    Finite bath-particle size and Minkowski sum The Boltzmann-Lorentz description (11) was written for point-like bath particles. If the bath particles are hard disks of diameterσ, their centers cannot approach the intruder closer than a distanceσ/2. The relevant excluded region f...

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    Regular polygon withnvertices A simple intruder is a polygon withnverticesv j placed at a distanceRfrom the origin: vj =R(cos(2πj/n),sin(2πj/n)), j= 0, . . . , n−1. (E9) 33 The casen= 3 yields an equilateral triangle,n= 4 a square, and in the limitn→ ∞a circle is recovered. It...

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    The vertices are v2j =R(cos 2πj/n,sin 2πj/n),v 2j+1 =r(cos(2πj/n+δ),sin(2πj/n+δ)), j= 0,

    Chiral and achiral wheel We now consider a possibly chiral intruder, modeled as a wheel withnteeth,i.e., a 2n-vertex polygon, with alternating outer and inner radiiRandr. The vertices are v2j =R(cos 2πj/n,sin 2πj/n),v 2j+1 =r(cos(2πj/n+δ),sin(2πj/n+δ)), j= 0, . . . , n−1.(E26)...

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