Pith Number

pith:FHB2TZBD

pith:2026:FHB2TZBDTOI55ZDMOUYVOZAJY3

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Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise

Francisco Monroy

Fluctuating endpoints in Hamilton's principle generate an effective Langevin force whose amplitude is filtered by the Hessian of the principal function.

arxiv:2605.17621 v1 · 2026-05-17 · cond-mat.stat-mech · physics.class-ph

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Claims

C1strongest claim

fluctuating endpoint data in Hamilton's principle induce fluctuations of the on-shell action. Hamilton--Jacobi propagation transports this boundary imprint, whose gradient generates an effective Langevin force inherited from boundary-action fluctuations. The resulting force is not freely specifiable: its amplitude is filtered by the Hessian of Hamilton's principal function, yielding multiplicative and state-dependent noise.

C2weakest assumption

The assumption that boundary fluctuations can be treated as independent variational data whose imprint survives Hamilton-Jacobi propagation without being washed out by the deterministic dynamics or requiring additional regularization; this enters when the paper states that the gradient of the fluctuating on-shell action directly supplies the Langevin force (abstract and implied § derivation).

C3one line summary

Fluctuating boundary data in Hamilton's principle propagate via Hamilton-Jacobi to produce state-dependent multiplicative Langevin forces, with additive noise recovered only after Markovian coarse-graining.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] L. D. Landau and E. M. Lifshitz,Mechanics, 3rd ed. (Pergamon Press, Oxford, 1976) 1976

[2] H. Goldstein, C. Poole, and J. Safko,Classical Mechan- ics, 3rd ed. (Addison-Wesley, San Francisco, 2002) 2002

[3] V. I. Arnold,Mathematical Methods of Classical Mechan- ics, 2nd ed. (Springer, New York, 1989) 1989

[4] Brillouin, Information and Control5, 223 (1962) 1962

[5] P.Langevin,ComptesRendusdel’AcadémiedesSciences 146, 530 (1908) 1908

Receipt and verification

First computed	2026-05-20T00:04:49.180342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29c3a9e4239b91dee46c7531576409c6e388f849a042ee9baa69d1c82e1053d7

Aliases

arxiv: 2605.17621 · arxiv_version: 2605.17621v1 · doi: 10.48550/arxiv.2605.17621 · pith_short_12: FHB2TZBDTOI5 · pith_short_16: FHB2TZBDTOI55ZDM · pith_short_8: FHB2TZBD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FHB2TZBDTOI55ZDMOUYVOZAJY3 \
  | 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: 29c3a9e4239b91dee46c7531576409c6e388f849a042ee9baa69d1c82e1053d7

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "648a5c800c3ad11eb324fc3fc77caf0dbb0c6a27b98b92b99e27f429381228bc",
    "cross_cats_sorted": [
      "physics.class-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-17T19:35:17Z",
    "title_canon_sha256": "16a4f1b722d59751e8fe5eaa9fa67513524e2e4b2cb692ee7036a874b93a88e3"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}