  For a small system like a colloidal particle or a single biomolecule embedded
in a heat bath, the optimal protocol of an external control parameter minimizes
the mean work required to drive the system from one given equilibrium state to
another in a finite time. In general, this optimal protocol obeys an
integro-differential equation. Explicite solutions both for a moving laser trap
and a time-dependent strength of such a trap show finite jumps of the optimal
protocol to be typical both at the beginning and the end of the process.
