  Harvesting free energy from the environment is essential for the operation of
many biological and artificial systems. We investigate the maximum rate of
harvesting achievable by optimizing a set of reactions in a Markovian system,
possibly given topological, kinetic, and thermodynamic constraints. We show
that the maximum harvesting rate can be expressed as a variational principle,
which we solve in closed-form for three physically meaningful regimes. Our
approach is relevant for optimal design and for quantifying efficiency of
existing reactions. Our results are illustrated on bacteriorhodopsin, a
light-driven proton pump from Archae, which is found to be close to optimal
under realistic conditions.
