This paper presents a study of the behavior of a one-dimensional system, with two potential minima separated by a barrier, coupled to a small set of harmonic oscillators. The time correlation function of equilibrium fluctuations in particle number (number correlation function) is found by computer simulation. An analogue of Kramers turnover in the barrier crossing rate is observed. The Grote-Hynes theory of non-Markovian rate processes provides a reasonable estimate for the rate constant at intermediate frictions. However, at high friction, the number correlation function becomes nonexponential, and the decay is much slower than expected from the Grote-Hynes theory. The model shows that close coupling to a small heat bath provides a mechanism for "internal friction".