  We study the condensation of closed string tachyons as a time-dependent
process. In particular, we study tachyons whose wave functions are either
space-filling or localized in a compact space, and whose masses are small in
string units; our analysis is otherwise general and does not depend on any
specific model. Using world-sheet methods, we calculate the equations of motion
for the coupled tachyon-dilaton system, and show that the tachyon follows
geodesic motion with respect to the Zamolodchikov metric, subject to a force
proportional to its beta function and friction proportional to the time
derivative of the dilaton. We study the relationship between world-sheet RG
flow and the solutions to our equations, finding a close relationship in the
case that the spatial theory is supercritical and the dilaton has a negative
time derivative.
