Pith Number

pith:VLRFXGAF

pith:2026:VLRFXGAFB6PAQODBHKBYN4THDI

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Hamiltonian flocks: Time-Reversal Symmetry and its consequences

Leticia F. Cugliandolo, Mathias Casiulis

Hamiltonian flocks obey a generalized time-reversal symmetry that produces a mixed fluctuation-dissipation theorem.

arxiv:2604.02914 v2 · 2026-04-03 · cond-mat.stat-mech

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Claims

C1strongest claim

The model obeys a generalized time-reversal symmetry that yields a fluctuation-dissipation theorem that mixes position and polarity degrees of freedom. Due to the oddness of spin under time reversal, the system also obeys Onsager-Casimir reciprocity rather than standard Onsager relations.

C2weakest assumption

The Hamiltonian flocks model is invariant under the specific generalized time-reversal operation defined by the authors, which relies on the conservative, non-Galilean structure of the model and the odd parity of polarity under that operation.

C3one line summary

Hamiltonian flocks obey a generalized time-reversal symmetry that yields a mixed fluctuation-dissipation theorem and Onsager-Casimir reciprocity, while naive time reversal produces spurious entropy production.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-07-01T01:18:24.613301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aae25b98050f9e0838613a8386f2671a03d369f2cac088acc5025f8bf74ad015

Aliases

arxiv: 2604.02914 · arxiv_version: 2604.02914v2 · doi: 10.48550/arxiv.2604.02914 · pith_short_12: VLRFXGAFB6PA · pith_short_16: VLRFXGAFB6PAQODB · pith_short_8: VLRFXGAF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VLRFXGAFB6PAQODBHKBYN4THDI \
  | 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: aae25b98050f9e0838613a8386f2671a03d369f2cac088acc5025f8bf74ad015

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5064516a7bc84eb704eb8ad6107a2463b57eb9cfec945385e83c4413c9c897b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-04-03T09:33:04Z",
    "title_canon_sha256": "ce4f69e478c97dedc3d187d0f443a15899f84e76c2aab443a5d8a7641eaabf20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.02914",
    "kind": "arxiv",
    "version": 2
  }
}