Pith Number

pith:FJYKHO44

pith:2026:FJYKHO44DHLPWAH65CV7OGPR3L

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Scaling Symmetry in Symplectic Thermodynamics

M.C. Baldiotti, R. Fresneda

Fixing a global scale variable recovers standard thermodynamics but requires breaking scale symmetry between energy and entropy for non-isothermal black hole dynamics.

arxiv:2605.12641 v1 · 2026-05-12 · math-ph · math.MP

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

Applying this framework to a Schwarzschild black hole reveals that breaking the scale symmetry between internal energy and entropy is a fundamental physical requirement to accommodate non-isothermal dynamics.

C2weakest assumption

That the constrained Hamiltonian dynamics unifies with symplectic and contact geometries such that the introduced global scale variable can be fixed to recover standard thermodynamics without altering the physical content of the Lagrangian submanifolds.

C3one line summary

Scaling symmetry is incorporated into thermodynamics via symplectic and contact geometries, yielding a diffeomorphism between ideal and van der Waals gas submanifolds and showing that scale symmetry between energy and entropy must break for non-isothermal Schwarzschild black hole dynamics.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] Bravetti,Contact geometry and thermodynamics, International Journal of Geometric Methods in Modern Physics16, No 2019

[2] M.C. Baldiotti, R. Fresneda, and C. Molina,A Hamiltonian approach to Thermodynamics, Annals of Physics 373, 245 (2016) 1, 2, 2 2016

[3] M. C. Baldiotti, R. Fresneda, C. Molina,A Hamiltonian approach for the Thermodynamics of AdS black holes, Annals of Physics382,22 (2017) 1, 5.2 2017

[4] R. Abraham and J. Marden,Foundations of Mechanics(Benjamin/Cummings Publishing Company, Mas- sachusetts, 1978) 3, 3.1, 4, 5.1 1978

[5] Weinstein,Symplectic manifolds and their lagrangian submanifolds, Advances in Mathematics6(3), 329 (1971) 3.1 1971

Receipt and verification

First computed	2026-05-18T03:09:59.987601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a70a3bb9c19d6fb00fee8abf719f1dafff355d9fc17a31974c92c827afb721b

Aliases

arxiv: 2605.12641 · arxiv_version: 2605.12641v1 · doi: 10.48550/arxiv.2605.12641 · pith_short_12: FJYKHO44DHLP · pith_short_16: FJYKHO44DHLPWAH6 · pith_short_8: FJYKHO44

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FJYKHO44DHLPWAH65CV7OGPR3L \
  | 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: 2a70a3bb9c19d6fb00fee8abf719f1dafff355d9fc17a31974c92c827afb721b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fb8313f00f1913536860c8cc7f8c62f45cc792cc954b01af4ee5d7bb4e8de47",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-12T18:31:12Z",
    "title_canon_sha256": "e7770b429ea3a926734946dc9629f86bfe262e6acee92612db1745d873b7012f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12641",
    "kind": "arxiv",
    "version": 1
  }
}