{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ec193fd4ef8e54c4dd240eb71ccd089a00f6d0e6d6ccd5f9254d773b2174ee2a","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"fcaef0f5ad4988bd4f295c80486ef5b54d70a6050a7af3b5dc186cef175e28cb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"stat.long-range-interactions.violent-relaxation-theory","kind":"phenomenon","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A self-gravitating cluster or a plasma that is suddenly disturbed settles quickly into a state that is not thermal. The classic Lynden-Bell theory predicts that state from statistics but often fails, and when and why it fails is not settled.","posed_since":"1967","precise":"For Vlasov dynamics of long-range systems (Hamiltonian mean-field model, 1D self-gravitating sheets, 3D gravitating N-body systems as $N\\to\\infty$), determine the conditions on initial data (virial ratio, waterbag levels) under which Lynden-Bell's maximum-entropy prediction of the quasi-stationary state is accurate, and give a predictive theory of the core-halo states produced when mixing is incomplete.","problem_ref":null,"references":"","settled_by":"A theory that predicts the quasi-stationary distribution function from initial data, tested against N-body simulations over a range of initial conditions.","status_note":"Lynden-Bell theory works for virialized initial states and parametric-resonance core-halo theory describes strongly non-virialized ones; a 2025 theory replaces global ergodicity by local mixing and predicts HMF quasi-stationary states with no fitted parameters (Teles, Pakter, Levin, arXiv:2501.15593).","title":"Predictive theory of collisionless violent 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