  We study the continuous limit of a multibox Erhenfest urn model proposed
before by the authors. The evolution of the resulting continuous system is
governed by a differential equation, which describes a diffusion process on a
circle with a nonzero drifting velocity. The short time behavior of this
diffusion process is obtained directly by solving the equation, while the long
time behavior is derived using the Poisson summation formula. They reproduce
the previous results in the large $M$ (number of boxes) limit. We also discuss
the connection between this diffusion equation and the Schr$\ddot{\rm o}$dinger
equation of some quantum mechanical problems.
