Pith Number

pith:S3L3ZR2X

pith:2026:S3L3ZR2XRIZOZYBLD6QY6W7JMK

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Duality Between Chemical Potential Dynamics and Reaction-Diffusion Systems

Daniel Zhou, Erwin Frey

Chemical-potential theories embed as slow manifolds in mass-conserving reaction-diffusion systems

arxiv:2605.15158 v1 · 2026-05-14 · cond-mat.soft

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

80 extracted · 80 resolved · 0 Pith anchors

[1] 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

[2] II D) Equations solved.For Figs

[3] IV A) Equations solved.In Figs

[4] V C) Equations solved.We integrate the original nonrecip- rocal two-component conserved dynamics [Eqs

[5] P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys.49, 435 (1977) 1977

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T21:40:25.417710Z
Last reissued	2026-05-17T21:57:18.739757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11

Aliases

arxiv: 2605.15158 · arxiv_version: 2605.15158v1 · pith_short_12: S3L3ZR2XRIZO · pith_short_16: S3L3ZR2XRIZOZYBL · pith_short_8: S3L3ZR2X

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/S3L3ZR2XRIZOZYBLD6QY6W7JMK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 96d7bcc7578a32ece02b1fa18f5be962bb113af074bbd164e3bc1651eaafda11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed6ff4199fe59fa2f233c909a935d9419b116de26f6e6dc4e43d242056f8e171",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.soft",
    "submitted_at": "2026-05-14T17:51:59Z",
    "title_canon_sha256": "adfcce83f903ff8b9d35d27c0c9868a82c42d45ce902750cf5921855aaca7921"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}