Strong Mpemba effect in interacting many-particle colloidal systems
In plain words
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.
Precise statement
$N$ 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.
What would settle it
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 in the literature
Unverified 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).