Stochastic control in microscopic nonequilibrium systems

From the manipulation of microscopic systems to the autonomous operation of molecular machines, quantifying nanoscale energy flows promises important insights in disciplines ranging from molecular biology to nanotechnology. A general understanding of the energetic costs of microscopic nonequilibrium processes would, for example, illuminate the design principles governing efficient biomolecular machines, and hence biological energy transduction. In recent years, considerable effort has gone into identifying deterministic control protocols that drive a system rapidly between states at minimum energetic cost. But for autonomous soft-matter systems, driving processes are themselves stochastic. Here we generalize a linear-response framework to incorporate such protocol variability, deriving a lower bound on the dissipation that is realized at finite protocol time. We illustrate our findings in several model systems.