Pith Number

pith:4EVNMFVW

pith:2026:4EVNMFVW3LBD7QL5WZQFSRAHIE

not attested not anchored not stored refs pending

The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure

Bob Osano

Factorization of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy.

arxiv:2605.00958 v2 · 2026-05-01 · cond-mat.stat-mech · math-ph · math.MP

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Claims

C1strongest claim

factorisation of the mesoscopic partition function across spatial cells is equivalent to extensivity of the coarse-grained free energy, with deviations governed by inter-cell correlations quantifiable via mutual information

C2weakest assumption

The coarse-graining into combined spatial and phase-space cells is valid for classical many-body systems and the fine-graining limit exactly recovers the canonical partition function without further restrictions on particle interactions or cell boundaries.

C3one line summary

A mesoscopic partition function equates factorization across spatial cells to extensivity of the coarse-grained free energy, with mutual-information corrections and a generalized Euler relation.

Cited by

2 papers in Pith

Entropy additivity from exponential decay of correlations: a coarse-grained operator approach

Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function

Receipt and verification

First computed	2026-06-02T01:03:47.869410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e12ad616b6dac23fc17db6605944074103eddc7675d559e3653a3f0bb2fe3d12

Aliases

arxiv: 2605.00958 · arxiv_version: 2605.00958v2 · doi: 10.48550/arxiv.2605.00958 · pith_short_12: 4EVNMFVW3LBD · pith_short_16: 4EVNMFVW3LBD7QL5 · pith_short_8: 4EVNMFVW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4EVNMFVW3LBD7QL5WZQFSRAHIE \
  | 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: e12ad616b6dac23fc17db6605944074103eddc7675d559e3653a3f0bb2fe3d12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1e39846721963461adcb6ba455e7faec6a052a32632eebf06324d6000860111",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-01T12:52:42Z",
    "title_canon_sha256": "f987d25987f9854d86eaacdac269d8d92931967f82c5b4555111cf87b312fc22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00958",
    "kind": "arxiv",
    "version": 2
  }
}