title: Optimal control of overdamped systems.
abstract: Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles underlying biological processes at the molecular level. Recent work has demonstrated that when a thermodynamic system is driven away from equilibrium then the space of controllable parameters has a Riemannian geometry induced by a generalized inverse diffusion tensor. We derive a simple, compact expression for the inverse diffusion tensor that depends solely on equilibrium information for a broad class of potentials. We use this formula to compute the minimal dissipation for two model systems relevant to small-scale information processing and biological molecular motors. In the first model, we optimally erase a single classical bit of information modeled by an overdamped particle in a smooth double-well potential. In the second model, we find the minimal dissipation of a simple molecular motor model coupled to an optical trap. In both models, we find that the minimal dissipation for the optimal protocol of duration τ is proportional to 1/τ, as expected, though the dissipation for the erasure model takes a different form than what we found previously for a similar system.
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA; Department of Mathematics, Berkeley City College, Berkeley, California 94704, USA; and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA.
authors.forename: Patrick R
authors.initials: PR
authors.lastname: Zulkowski
authors.affiliation: Department of Physics, University of California, Berkeley, California 94720, USA; Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA; and Helen Wills Neuroscience Institute, University of California, Berkeley, California 94720, USA.
authors.forename: Michael R
authors.initials: MR
authors.lastname: DeWeese
mesh_terms: D004058:Diffusion; D019277:Entropy; D008962:Models, Theoretical; D020409:Molecular Motor Proteins / Q000737:chemistry
chemical_list: D020409:Molecular Motor Proteins