{"paper":{"title":"The fractal dimension of Brownian dynamics in liquids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Fluid memory effects redefine the fractal dimension of Brownian velocity fluctuations to 7/4.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Giuseppe Procopio, Jason Boynewicz, Mark G. Raizen, Massimiliano Giona, Michael C. Thumann","submitted_at":"2026-05-15T17:56:47Z","abstract_excerpt":"The classical Einstein-Langevin theory of Brownian motion assumes a memoryless thermal bath, establishing a universal fractal dimension of $d_v = 3/2$ for the velocity fluctuations of a particle. In this Letter, we demonstrate experimentally and theoretically that fluid-inertial memory effects fundamentally redefine the fractal scaling of these fluctuations. In analyzing highly resolved measurements of Brownian microspheres in liquids, we show that the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of $d_v = 7/4$. Coupled with theoretical analysis of"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of dv = 7/4","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Brownian velocity fluctuations in liquids have fractal dimension 7/4 due to non-Markovian hydrodynamic thermal noise, establishing a new non-equilibrium universality class.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fluid memory effects redefine the fractal dimension of Brownian velocity fluctuations to 7/4.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2b4a66948cb6eb4629803a97b75824e6ce5d1ab3fda783f3ecb7d06f41054140"},"source":{"id":"2605.16252","kind":"arxiv","version":1},"verdict":{"id":"29219584-6d5b-4387-931f-9a5ce6740364","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:25:44.069487Z","strongest_claim":"the non-Markovian hydrodynamic thermal noise establishes a distinct velocity fractal dimension of dv = 7/4","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Fluid memory effects redefine the fractal dimension of Brownian velocity fluctuations to 7/4."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16252/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:18.699564Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:30:46.994797Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:42.174098Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:41.786335Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:23.080629Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:23.935443Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.595744Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T16:51:56.264496Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"593a8027e0a16a7efbbe7bdad9dc208356e8fcd2c691a889ea26121fd20a284b"},"references":{"count":52,"sample":[{"doi":"","year":null,"title":"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","work_id":"159be7e5-ee35-457d-9d47-af31458773a8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"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","work_id":"35521d6a-a8e0-4f2b-89d4-7f22222a0bc5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Moreover, it follows from eq","work_id":"ec610365-e89c-4a07-b390-d506da55de05","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"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","work_id":"466b1012-4b8e-4b67-97d9-26a8f468517e","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Boynewicz et al","work_id":"118e9e22-2472-443d-90b7-33da8c57d93c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":52,"snapshot_sha256":"36abc101233a1a7a00dfed5c6a27121069a747f55265ee907522fde923603eb8","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"cd49bcb75e9e0c867bd6ae087f56e8e9e27fc61385df9845ac9ae381df3e085f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}