{"id":"a37225a6-a887-4a06-a0ce-bcb97f1a0d32","arxiv_id":"2606.10486","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Derives stress tensors for ABP+TRI via Lagrange equations, confirms inertia-dependent EOS in periodic 2D simulations, shows confinement breakdown from polarization, and excludes swim stress from local tensor.","lead":"This paper derives virial stress tensors for active Brownian particles that include translational and rotational inertia, using Lagrange equations for periodic and confined systems. Simulations show an inertia-dependent equation of state holds in periodic boundaries but breaks under confinement due to wall polarization, and that swim stress is excluded from the local stress tensor.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Derivation via Lagrange's equations of the first kind may omit activity-induced stress terms from self-propulsion","rationale":"The reader's weakest assumption directly identifies the load-bearing step: whether the Lagrange framework for rotational inertia introduces or omits activity-induced terms. This matches the strongest claim about swim-stress exclusion and is the point least secured by the given derivation method and ideal-gas simulations.","tokens_in":1699,"tokens_out":373,"duration_ms":31381,"concrete_test":"Re-derive the local stress tensor from the inertial Langevin equations (including explicit active force F_a = v0 u(θ) and rotational inertia) via the standard Irving-Kirkwood or momentum-balance route; compare term-by-term to the expression obtained from Lagrange's equations of the first kind. If a swim-stress-like term proportional to r ⊗ F_a appears in the former but is absent in the latter, the exclusion is method-dependent.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim—that the swim stress is not included in the derived local stress tensor for ABP+TRIs, and is thus not representative—rests on applying Lagrange's equations of the first kind specifically to the rotational motion in 2D. This assumes the standard constrained Lagrangian setup for inertia fully accounts for all contributions without extra terms generated by the orientation-dependent active force (F = v0 · u(θ)). Because activity is non-conservative and couples translation to rotation, the momentum flux or virial expression could acquire additional activity-induced contributions not captured by the passive Lagrange construction; if present, their omission would make the exclusion of swim stress an artifact of the chosen formalism rather than a general result. Simulations are restricted to the ideal (non-interacting) gas, leaving open whether the same exclusion holds once pair forces are added.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper derives local stress tensors for active Brownian particles with translational and rotational inertia (ABP+TRI) in both periodic and wall-confined geometries by applying Lagrange's equations of the first kind to the rotational degrees of freedom. Langevin simulations of a 2D ideal active gas confirm an inertia-dependent equation of state under periodic boundaries; confinement produces wall-induced polarization and density buildup that breaks the EOS globally while preserving bulk stress equivalence. The central result is that the swim stress does not appear in the derived local stress tensor for either boundary condition.","tokens_in":1872,"tokens_out":534,"duration_ms":14024,"significance":"If the derivation is complete, the finding that swim stress is excluded from the local tensor supplies a concrete counter-example to its general use as a stress measure in inertial active systems and supplies an explicit inertia-dependent EOS for the ideal case. The simulation confirmation for the ideal gas is a clear strength; the result would be more impactful if shown to survive pair interactions.","major_comments":[{"comment":"The derivation (described in the abstract and the methods section on Lagrange's equations of the first kind) starts from the standard constrained Lagrangian for rotational motion and reports that the active force F = v0 · u(θ) contributes no additional terms to the virial expression. Because the active force is non-conservative and orientation-dependent, an explicit expansion of the momentum flux (or the full Irving-Kirkwood-style stress) is required to demonstrate that no activity-induced contributions are omitted by construction; without that step the exclusion of swim stress remains tied to the chosen formalism rather than shown to be general.","section":"derivation via Lagrange's equations of the first kind"},{"comment":"Simulations are performed exclusively for the ideal (non-interacting) gas. The claim that swim stress is not representative 'in general' for ABP+TRI systems therefore rests on an extrapolation from the non-interacting limit; the manuscript should either restrict the scope of the claim or supply at least one interacting case (e.g., repulsive disks) to test whether pair forces reintroduce swim-stress-like contributions.","section":"Langevin simulations of an ideal active gas"}],"minor_comments":[{"comment":"The abstract states that the local stress in the bulk of confined systems is 'identical' to the periodic case; a quantitative plot or table comparing the two bulk values (with error bars) would make the statement precise.","section":"confinement results"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments. We address each major point below and outline revisions to clarify the derivation and scope of the claims.","responses":[{"response":"We agree that an explicit expansion of the momentum flux would strengthen the argument. In the revised manuscript we will add a dedicated subsection deriving the local stress tensor from the full equations of motion (including the active force term), showing term-by-term that the orientation-dependent active force does not enter the virial contribution under the Lagrange multiplier treatment of the rotational constraint. This will make clear that the exclusion follows from the structure of the momentum balance rather than being an artifact of the formalism alone.","revision_made":"yes","referee_comment":"[derivation via Lagrange's equations of the first kind] The derivation starts from the standard constrained Lagrangian for rotational motion and reports that the active force F = v0 · u(θ) contributes no additional terms to the virial expression. Because the active force is non-conservative and orientation-dependent, an explicit expansion of the momentum flux (or the full Irving-Kirkwood-style stress) is required to demonstrate that no activity-induced contributions are omitted by construction; without that step the exclusion of swim stress remains tied to the chosen formalism rather than shown to be general."},{"response":"The stress-tensor derivation itself is independent of particle interactions: any conservative pair potentials enter the virial expression through the standard potential term and do not alter the treatment of the active force. Nevertheless, we acknowledge that the numerical confirmation is limited to the ideal gas. In revision we will restrict the phrasing of the 'in general' claim to the ideal case while noting that the analytic result holds for interacting systems; we do not add new interacting simulations at this stage.","revision_made":"partial","referee_comment":"[Langevin simulations of an ideal active gas] Simulations are performed exclusively for the ideal (non-interacting) gas. The claim that swim stress is not representative 'in general' for ABP+TRI systems therefore rests on an extrapolation from the non-interacting limit; the manuscript should either restrict the scope of the claim or supply at least one interacting case (e.g., repulsive disks) to test whether pair forces reintroduce swim-stress-like contributions."}],"tokens_in":1428,"tokens_out":487,"duration_ms":15234,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The key point is that including translational and rotational inertia in active Brownian particles produces a local stress tensor that leaves out the swim stress for both periodic boundaries and walls. The derivation uses Lagrange's equations of the first kind on the rotational motion, and 2D Langevin runs on an ideal active gas confirm an inertia-dependent equation of state in periodic systems. Confinement adds wall polarization and density buildup that grows with rotational inertia, breaking the EOS near the walls while the bulk stress stays the same as the periodic case.\n\nWhat stands out is the explicit treatment of rotational inertia in the stress expression and the direct comparison of boundary conditions. The simulations line up with the periodic derivation, which is useful for anyone extending virial calculations in active systems.\n\nThe main limitation is the restriction to non-interacting particles. Pair forces are not tested, so it is unclear whether the swim-stress exclusion survives once interactions are present. The stress-test concern about activity-induced terms also lands: the active force is non-conservative and orientation-dependent, and applying standard Lagrange equations to rotation might omit extra contributions to the momentum flux. Without the full equations in view it is hard to rule that out, and the claim that swim stress is not representative in general rests on this choice of formalism.\n\nThis is for people already working on stress tensors in active matter or inertial colloidal systems. A reader who needs to compute local stress under confinement or with inertia will find the boundary comparison and the inertia dependence worth checking. It is formally grounded enough and specific enough to deserve referee time, even if revisions are likely on the derivation and the ideal-gas restriction.","headline":"The paper derives a local virial stress for ABPs with both translational and rotational inertia that excludes swim stress in periodic and confined cases, backed by ideal-gas simulations, but the non-interacting limit and Lagrange setup raise questions about missing activity terms.","tokens_in":2330,"tokens_out":419,"would_cite":false,"duration_ms":15348,"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":"The swim stress is not included in the local stress tensor for active Brownian particles with translational and rotational inertia.","keywords":["active Brownian particles","virial stress","swim stress","translational inertia","rotational inertia","equation of state","confinement","Langevin simulations"],"falsifier":"A simulation measurement in which the local stress tensor computed from particle trajectories equals the same tensor plus an explicit swim-stress contribution would falsify the central claim.","tokens_in":2606,"feed_emoji":"","tokens_out":683,"duration_ms":23763,"temperature":0.7,"pith_summary":"This paper derives the stress tensor for active Brownian particles that also have translational and rotational inertia using Lagrange's equations of the first kind for rotational motion. It shows that an equation of state exists for periodic boundary conditions that depends on the inertia parameters in general. When particles are confined between walls, polarization of the propulsion direction and density enhancement near the walls both increase with rotational inertia, which modifies the normal component of the local stress and breaks the equation of state. The bulk stress in the confined case still matches the periodic result. Crucially the swim stress does not appear in the local stress tensor for either boundary condition.","feed_headline":"Swim stress excluded from local stress tensor in inertial active particles","feed_subtitle":"Periodic systems follow an inertia-dependent equation of state; confinement breaks it via wall polarization, yet swim stress stays out in bo","key_machinery":"The local virial stress tensor derived from Lagrange's equations of the first kind applied to the rotational motion of the particles.","core_discovery":"Stress tensors for ABP+TRI systems are obtained via Lagrange's equations of the first kind for rotational motion, both for periodic conditions and wall confinement. Langevin simulations of an ideal active gas in 2D verify an inertia-dependent equation of state under periodic boundaries. Confinement produces strong near-wall polarization of propulsion and elevated density that scale with rotational inertia, modifying the local normal stress and violating the equation of state; nevertheless the bulk stress matches the periodic result. The swim stress is absent from the local stress tensor under both boundary conditions, indicating it does not represent the stress in ABP+TRI systems.","pith_inferences":["Inertial active-matter models may need to recompute stress without relying on swim-stress estimates when particles have mass or moment of inertia.","Pressure measurements in confined inertial active colloids should compare directly against the derived local tensor rather than swim-stress formulas.","The exclusion may or may not persist in three dimensions or when particle interactions are added."],"forward_implications":["Periodic systems obey an equation of state that depends on both translational and rotational inertia.","Confinement produces rotational-inertia-dependent polarization of propulsion direction and density buildup near walls.","This polarization alters the local stress tensor component normal to the walls and breaks the equation of state.","Bulk stress inside confined systems remains identical to the periodic-system stress.","The swim stress is excluded from the local stress tensor for both periodic and confined boundary conditions."],"fun_headline_variants":["Swim stress omitted from local tensor in ABP+TRI systems","Inertia sets equation of state for periodic active particle systems","Confinement breaks inertia EOS via wall polarization in active gas","Bulk stress matches periodic while swim stress stays out in ABP+TRI","Lagrange equations give stress for inertial active Brownian particles"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Lagrange's equations of the first kind for rotational motion capture all relevant inertial contributions without additional activity-induced terms.","fun_headline_variants_meta":{"raw":{"variants":["Swim stress omitted from local tensor in ABP+TRI systems","Inertia sets equation of state for periodic active particle systems","Confinement breaks inertia EOS via wall polarization in active gas","Bulk stress matches periodic while swim stress stays out in ABP+TRI","Lagrange equations give stress for inertial active Brownian particles"]},"model":"grok-4.3","cost_usd":0.003506,"raw_usage":{"total_tokens":1850,"prompt_tokens":680,"num_sources_used":0,"completion_tokens":84,"cost_in_usd_ticks":35062000,"prompt_tokens_details":{"text_tokens":680,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1086,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":680,"tokens_out":84,"duration_ms":11298,"temperature":1.0,"reasoning_tokens":1086,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T11:46:11.122598+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation measurement in which the local stress tensor computed from particle trajectories equals the same tensor plus an explicit swim-stress contribution would falsify the central claim.","supporting_citations":[],"review_version":1}