  A single vortex overcoming the surface barrier in a mesoscopic superconductor
with lateral dimensions of several coherence lengths and thickness of several
nanometers provides an ideal platform to study thermal activation of a single
vortex. In the presence of thermal fluctuations, there is non-zero probability
for vortex penetration into or exclusion from the superconductor even when the
surface barrier does not vanish. We consider the thermal activation of a single
vortex in a mesoscopic superconducting disk of circular shape. To obtain
statistics for the penetration and exclusion magnetic fields, slow and periodic
magnetic fields are applied to the superconductor. We calculate the
distribution of the penetration and exclusion fields from the thermal
activation rate. This distribution can also be measured experimentally, which
allows for a quantitative comparison.
