  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 modelled 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 is
inversely proportional to protocol duration, as expected, though the
dissipation for the erasure model takes a different form than what we found
previously for a similar system.
