  We report a new phenomenon, called self-recovery, in the process of diffusion
in a region with boundary. Suppose that a diffusing quantity is uniformly
distributed initially and then gets excited by the change in the boundary
values over a time interval. When the boundary values return to their initial
values and stop varying afterwards, the value of a physical quantity related to
the diffusion automatically comes back to its original value. This
self-recovery phenomenon has been discovered and fairly well understood for
finite-dimensional mechanical systems with viscous damping. In this paper, we
show that it also occurs in the process of diffusion. Several examples are
provided from fluid flows, quasi-static electromagnetic fields and heat
conduction. In particular, our result in fluid flows provides a dynamic
explanation for the famous experiment by Sir G.I. Taylor with glycerine in an
annulus on kinematic reversibility of low-Reynolds-number flows.
