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Our method applies to equilibrium dynamics, where it recovers and complements existing results, but also extends to their non-equilibrium counterparts. We explain how non-linear terms can be systematically computed a"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Using a well-chosen definition for the interface and the dynamical-action formalism to represent path probabilities, we derive the linear relaxation of the interface and the fluctuations around it for a large class of models. Our method applies to equilibrium dynamics, where it recovers and complements existing results, but also extends to their non-equilibrium counterparts.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The interface remains weakly deformed and the two phases stay stable, so that the fluctuating hydrodynamics plus dynamical-action formalism can be projected onto interface coordinates without uncontrolled approximations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives interface dynamics and fluctuations from bulk fluctuating hydrodynamics for equilibrium and non-equilibrium models, with a warning on a popular ansatz for active systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A dynamical-action approach derives linear interface relaxation and fluctuations from bulk hydrodynamics for both equilibrium and non-equilibrium systems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0a918664dce549c8f3da56852d0e6ea01a25d0164c2eb8dc902858479b283dcf"},"source":{"id":"2605.16503","kind":"arxiv","version":1},"verdict":{"id":"18f85d9b-c763-45c0-b85e-d2ce68e1d86a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:18:10.331252Z","strongest_claim":"Using a well-chosen definition for the interface and the dynamical-action formalism to represent path probabilities, we derive the linear relaxation of the interface and the fluctuations around it for a large class of models. 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