Jara's mixing-time conjecture for particle-conserving systems on the circle

Consider a particle-conserving system on a circle of size $N$ with positive density, nice local interactions, and average current whose second derivative does not vanish.

Jara's conjecture. The mixing time is of order

$$N^{3/2},$$

possibly up to poly-logarithmic corrections.

This conjecture proposes that the $N^{3/2}$ mixing-time scale extends beyond asymmetric exclusion processes to a broad class of particle-conserving systems. It is attributed to Milton Jara, and the source does not state whether it has been resolved.