  Biological systems fundamentally exist out of equilibrium in order to
preserve organized structures and processes. Many changing cellular conditions
can be represented as transitions between nonequilibrium steady states, and
organisms have an interest in optimizing such transitions. Using the
Hatano-Sasa Y-value, we extend a recently developed geometrical framework for
determining optimal protocols so that it can be applied to systems driven from
nonequilibrium steady states. We calculate and numerically verify optimal
protocols for a colloidal particle dragged through solution by a translating
optical trap with two controllable parameters. We offer experimental
predictions, specifically that optimal protocols are significantly less costly
than naive ones. Optimal protocols similar to these may ultimately point to
design principles for biological energy transduction systems and guide the
design of artificial molecular machines.
