Pith Number

pith:SITQBIBD

pith:2026:SITQBIBDFGKOEYDMVFABATH4ZR

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Linearization Principle: The Geometric Origin of Nonlinear Fokker-Planck Equations

Hiroki Suyari

The Linearization Principle derives nonlinear Fokker-Planck equations geometrically by keeping the drift term linear in probability density.

arxiv:2603.01278 v3 · 2026-03-01 · cond-mat.stat-mech · math-ph · math.MP

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Claims

C1strongest claim

By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the q-deformed geometry... exhibits a fundamental duality between the dynamic index q and the thermodynamic index 2-q.

C2weakest assumption

The Linearization Principle itself, introduced directly at the dynamical stage as the central geometric rule that forces the drift to stay linear while allowing nonlinear diffusion.

C3one line summary

A geometric Linearization Principle derives nonlinear Fokker-Planck equations that preserve linear drift and Einstein relation while producing q-Gaussian equilibria minimizing a 2-q entropy functional.

Formal links

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Receipt and verification

First computed	2026-05-25T02:01:16.303146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf

Aliases

arxiv: 2603.01278 · arxiv_version: 2603.01278v3 · doi: 10.48550/arxiv.2603.01278 · pith_short_12: SITQBIBDFGKO · pith_short_16: SITQBIBDFGKOEYDM · pith_short_8: SITQBIBD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SITQBIBDFGKOEYDMVFABATH4ZR \
  | 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: 922700a0232994e2606ca940104cfccc5a5f3fd0972e9e425d075b3388405ddf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb35f431741fb86a7174caad71c85be80afe78c4f1ea0e09852d922d5b24c308",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-03-01T21:31:32Z",
    "title_canon_sha256": "0fc39303bc78b900729d2ec80210f5d19052bf98b8f04d4d3fd6697d56ae4465"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.01278",
    "kind": "arxiv",
    "version": 3
  }
}