Pith Number

pith:6C5CKYG2

pith:2026:6C5CKYG2FCPRJTXI6BAFB6YN2M

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Hydrodynamic Initial Conditions in Small Systems from Proton Phase-Space Entropy

Gabriel Rabelo-Soares, Giorgio Torrieri, Gojko Vujanovic

The Wehrl entropy from coarse-graining the proton's phase-space distribution supplies the entropy current required for relativistic hydrodynamics in small collision systems.

arxiv:2604.12691 v1 · 2026-04-14 · hep-ph · nucl-th

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Claims

C1strongest claim

This entropy provides a semi-classical, positive-definite measure of the density of accessible microstates at a given resolution scale, and therefore constitutes the appropriate quantity to characterize entropy deposition in small collision systems.

C2weakest assumption

That coarse-graining the proton phase-space distribution with Wehrl entropy produces an entropy current that correctly matches the requirements of relativistic hydrodynamics without additional assumptions about the resolution scale or the degree of mixing.

C3one line summary

Wehrl entropy from coarse-graining the proton phase-space distribution supplies the appropriate initial entropy for hydrodynamics in small systems.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] Collective flow and viscosity in relativistic heavy-ion collisions.Ann 2013 · doi:10.1146/annurev-nucl-102212-170540

[2] J. L. Nagle, W. A. Zajc, Small System Collectivity in Relativistic Hadronic and Nuclear Collisions, Ann. Rev. Nucl. Part. Sci. 68 (2018) 211–235. arXiv:1801.03477, doi:10.1146/annurev-nucl-101916-1232 2018 · doi:10.1146/annurev-nucl-101916-123209

[3] A. Collaboration, Measurement of long-range multiparticle azimuthal correlations with the subevent cumulant method in $pp$ and $p$+Pb collisions with the ATLAS detector at the CERN Large Hadron Collid 2018 · doi:10.1103/physrevc.97.024904

[4] G. Rabelo-Soares, G. Vujanovic, G. Torrieri, Characterizing the initial state of hydrodynamics in pp and pA colli- sions (11 2025). arXiv:2511.03851 2025

[5] Einstein-Podolsky-Rosen Paradox and Quantum Entanglement at Subnucleonic Scales, 2020 · doi:10.1103/physrevlett.124.062001

Receipt and verification

First computed	2026-05-28T02:04:47.605333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0ba2560da289f14cee8f04050fb0dd333bea70d14f5488017a4b445cf732fdb

Aliases

arxiv: 2604.12691 · arxiv_version: 2604.12691v1 · doi: 10.48550/arxiv.2604.12691 · pith_short_12: 6C5CKYG2FCPR · pith_short_16: 6C5CKYG2FCPRJTXI · pith_short_8: 6C5CKYG2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6C5CKYG2FCPRJTXI6BAFB6YN2M \
  | 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: f0ba2560da289f14cee8f04050fb0dd333bea70d14f5488017a4b445cf732fdb

Canonical record JSON

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    "cross_cats_sorted": [
      "nucl-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-04-14T13:02:33Z",
    "title_canon_sha256": "43b435f8fd98dc06a6f6ce9ac15c8f0b8e315c11e905fcb03c38fd96e6e37d55"
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  "source": {
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    "version": 1
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}