Universal bounds on optimization of free energy harvesting

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.