  In many systems, the time scales of the microscopic dynamics and macroscopic
dynamics of interest are separated by many orders of magnitude. Examples
abound, for instance nucleation, protein folding, and chemical reactions. For
these systems, direct simulation of phase space trajectories does not
efficiently determine most physical quantities of interest. The last decade has
seen the advent of methods circumventing brute force simulation. For most
dynamical quantities, these methods all share the drawback of systematical
errors. We present a novel method for generating ensembles of phase space
trajectories. By sampling small pieces of these trajectories in different phase
space domains and piecing them together in a smart way using equilibrium
properties, we obtain physical quantities such as transition times. This method
does not have any systematic error and is very efficient; the computational
effort to calculate the first passage time across a free energy barrier does
not increase with the height of the barrier. The strength of the method is
shown in the Ising model. Accurate measurements of nucleation times span almost
ten orders of magnitude and reveal corrections to classical nucleation theory.
