Pith Number

pith:MSLCWVAQ

pith:2026:MSLCWVAQ4OOC7LMTQONLU2CJDE

not attested not anchored not stored refs resolved

The fractal dimension of Brownian dynamics in liquids

Giuseppe Procopio, Jason Boynewicz, Mark G. Raizen, Massimiliano Giona, Michael C. Thumann

Fluid memory effects redefine the fractal dimension of Brownian velocity fluctuations to 7/4.

arxiv:2605.16252 v1 · 2026-05-15 · cond-mat.stat-mech

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Claims

C1strongest claim

the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of dv = 7/4

C2weakest assumption

That the highly resolved measurements of Brownian microspheres in liquids accurately capture the initial scaling of the velocity autocorrelation function without significant experimental artifacts or post-selection effects.

C3one line summary

Brownian velocity fluctuations in liquids have fractal dimension 7/4 due to non-Markovian hydrodynamic thermal noise, establishing a new non-equilibrium universality class.

References

52 extracted · 52 resolved · 1 Pith anchors

[1] In the Einstein-Langevin approach, the dynamics are Markovian and the particle’s velocity is a stochastic pro- cess possessing the fractal dimension dv = 3 / 2

[2] fails to interpret some relevant features of Brownian dynamics in liquid, such as the scaling of the velocity autocorrelation func- tion. In Newtonian liquids, such as water or acetone at room tempera

[3] Moreover, it follows from eq

[4] that the Basset kernel displays a singularity at τ = 0. This singularity is the conse- quence of another paradox of inﬁnite velocity of propa- gation [16], speciﬁcally that of the shear stresses, that

[5] Boynewicz et al

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:00.217193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64962b5410e39c2fad93839aba6849193ec200fb3923a02f30797bd9aef4d0e0

Aliases

arxiv: 2605.16252 · arxiv_version: 2605.16252v1 · doi: 10.48550/arxiv.2605.16252 · pith_short_12: MSLCWVAQ4OOC · pith_short_16: MSLCWVAQ4OOC7LMT · pith_short_8: MSLCWVAQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MSLCWVAQ4OOC7LMTQONLU2CJDE \
  | 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: 64962b5410e39c2fad93839aba6849193ec200fb3923a02f30797bd9aef4d0e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd6cf095109a2147aab03cd04c5526a2f6f207f7c061a6ecb05d8337dc080e0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-15T17:56:47Z",
    "title_canon_sha256": "daa1e7be55aa5bde0b14a4ea0679e37f4c47f2c07617e9c68ffe0584c05a7236"
  },
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  "source": {
    "id": "2605.16252",
    "kind": "arxiv",
    "version": 1
  }
}