{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"56ed8b15662b45b8662467a0c1c69ccf0c336d42631c93fa0cbe6f169b0754e1","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["3b1aa32af3486e7ba53b0a7f3b6cc59b97392913134703a17bedb01f3145575a","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"2cd298a5fa6977c02b9af9084c801fbc967c79ebb2bc9aef02400fd4f6d66886","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.long-range-interactions.dynamical-long-range-threshold","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Interactions that fall off with distance as $1/r^\\alpha$ behave as long-range in thermodynamics when $\\alpha$ is below the space dimension, but the threshold for long-lived non-equilibrium states may differ. The exact boundary is not established.","posed_since":"2010","precise":"For particles in $d$ dimensions with pair potential $V(r) \\sim 1/r^{\\alpha}$, determine the range of $\\alpha$ for which the $N \\to \\infty$ dynamics follows a Vlasov equation with quasi-stationary states whose lifetime diverges with $N$, as opposed to collisional relaxation on $N$-independent times; the proposed criterion is $\\alpha < d - 1$ (force integrable at large distance). An answer is a classification with proof or with simulations controlling $N \\to \\infty$.","problem_ref":"3b1aa32af3486e7ba53b0a7f3b6cc59b97392913134703a17bedb01f3145575a","references":"","settled_by":"A kinetic-theory derivation of the $N$ dependence of relaxation times for general $\\alpha$, confirmed by simulations in $d = 1, 2, 3$.","status_note":"The criterion was proposed by Gabrielli, Joyce and Marcos (Phys. Rev. Lett. 105, 210602, 2010); a derivation for general $\\alpha$ and $d$ is incomplete.","title":"Which power-law decays make interactions dynamically long-range?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b9bfae21f6445bc1318229a5131aa602c720f08572521aa5ad41ee83b60537be","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"db8302b6d38de4487c8e1ba701781fa4010fffc0ee85482b29748f95d7ba1dec","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"QoW6zPSUycnvaTmdoxPbza64wSKl3YFJiUCe0-mMucX8J5D_zrSmcYmbl0fG158J4pwBOn-z42sqq5ws3X3WAg"},"schema":"pubphys.envelope/1"},"record_hash":"b9bfae21f6445bc1318229a5131aa602c720f08572521aa5ad41ee83b60537be","leaf_index":3794}