{"paper":{"title":"Duality Between Chemical Potential Dynamics and Reaction-Diffusion Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Daniel Zhou, Erwin Frey","submitted_at":"2026-05-14T17:51:59Z","abstract_excerpt":"Pattern formation in soft, active, and biological matter is described by two ostensibly distinct continuum frameworks: phase-field theories driven by chemical-potential gradients, and mass-conserving reaction-diffusion (McRD) dynamics governed by local interconversion kinetics. Here we establish a constructive, equation-level duality valid in the nonlinear, far-from-equilibrium regime. McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullclin"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9fe2b3308d7e2644550864d22411ce7ae1855c026063d67baae8a3302f12980a"},"source":{"id":"2605.15158","kind":"arxiv","version":1},"verdict":{"id":"bca65b59-da87-465c-8b64-77ec6a16e908","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:14:42.711089Z","strongest_claim":"McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline.","one_line_summary":"An exact equation-level duality maps every conserved chemical-potential theory onto the slow manifold of a mass-conserving reaction-diffusion system and recovers the chemical-potential form from any McRD system with an attractive nullcline in the fast-interconversion limit.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that an attracting manifold exists for the slow dynamics and that the nullcline is attractive in the fast-interconversion limit, allowing the exact embedding and recovery of the chemical-potential representation.","pith_extraction_headline":"Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems"},"references":{"count":80,"sample":[{"doi":"","year":null,"title":"The source–sink term is expanded in the same way as before, s(ϕ) =s α +s ′ α δϕ+O(δϕ 2),(C14) ForD m = 0 (so thatD c =M), the linearized dynamics read ∂tδc=M∇ 2δc−A c δc−A m δm+s α +s ′ αδϕ,(C15a) ∂tδ","work_id":"cf35591c-7e80-4cf6-a5e5-621a26cecf87","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"II D) Equations solved.For Figs","work_id":"4729944e-b8fd-48a1-b2ad-dc491a2cfd31","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"IV A) Equations solved.In Figs","work_id":"5c326fd1-8db8-4ca4-8ea2-17300fabbb01","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"V C) Equations solved.We integrate the original nonrecip- rocal two-component conserved dynamics [Eqs","work_id":"ae4a8c5e-86fb-4236-943f-edc5054484dc","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1977,"title":"P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys.49, 435 (1977)","work_id":"365934ad-efbe-450d-b219-34fa57437107","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":80,"snapshot_sha256":"37b677025ce4e7b0a3584da648514a8893cca69a4875d84dfdd407dd4b90209f","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f1ba3ceb054fea37d1ff5ccc1ad8e89d424d67d0302a16f7fa5d57bcce2847f1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}