  We study the autocorrelations of observables constructed from the topological
charge density, such as the topological charge on a time slice or in a
subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge
theory with both periodic and open boundary conditions. We show that the
autocorrelation functions of these observables obey a simple diffusion equation
and we measure the diffusion coefficient, finding that it scales like the
square of the lattice spacing. We use this result and measurements of the rate
of tunneling between topological charge sectors to calculate the scaling
behavior of the autocorrelation times of these observables on periodic and open
lattices. There is a characteristic lattice spacing at which open boundary
conditions become worthwhile for reducing autocorrelations and we show how this
lattice spacing is related to the diffusion coefficient, the tunneling rate,
and the lattice Euclidean time extent.
