{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"aafba884c263be3e0b96fec08ae684e3f80664bab2513aeeb251c32780f9b2d0","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"086130d95d78899144b27fb2e3d94110eb908f389d3f087e6e20746b9037f7eb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"stat.mpemba-relaxation.colloid-many-body","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Exponentially faster cooling has been seen for one microscopic bead moving in a carefully shaped energy landscape. The question is whether the same effect exists, and can be measured, for many interacting beads, where the slowest relaxation is collective.","posed_since":"","precise":"$N$ overdamped Brownian particles with pair potential $u(r)$ in an external potential $U(x)$ at fixed density, bath temperature $T_{b}$, initial equilibrium at $T_{0} > T_{b}$. For the $N$-body Fokker-Planck generator, let $a_{2}(T_{0})$ be the amplitude of the slowest nontrivial mode. Does a zero $a_{2}(T_{0}) = 0$ with $T_{0} > T_{b}$ exist and persist as $N \\to \\infty$ with the gap ratio $\\lambda_{3}/\\lambda_{2}$ bounded above 1, and is it visible in a collective observable? An answer is yes or no for a stated class of $u$ and $U$, with the scaling of the speedup with N.","problem_ref":null,"references":"","settled_by":"An exact or numerical spectral analysis of the $N$-body generator showing the fate of the $a_2$ zero as $N$ grows, confirmed by an experiment on an interacting colloidal suspension.","status_note":"Experiments to date use a single particle in a tailored one-dimensional potential (Kumar and Bechhoefer, Nature 2020; inverse effect, Kumar, Chetrite and Bechhoefer, PNAS 2022), simulations of a few interacting trapped colloids report a double Mpemba effect (Malhotra and Lowen, J. Chem. Phys. 2024), and a 2026 preprint finds the effect without potential walls only above a critical quench rate (Sane and Bechhoefer, arXiv:2609.32871).","title":"Strong Mpemba effect in interacting many-particle colloidal 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