UC Berkeley

Living systems are distinguished by their self-organization. Given the entropic driving force embodied in the second law of thermodynamics, creating and maintaining such organization requires staying far from equilibrium. Furthermore, since selective advantage may be incurred by energetically-efficient operation, evolution may have sculpted biological components to interact so as to reduce the energy wasted during transitions. Therefore, a deeper understanding of the principles governing biological molecular machines and their synthetic counterparts may be achieved by cultivating a set of tools to explore the optimization of finite-time nonequilibrium transitions of mesoscopic systems.

Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. Optimal protocols are equivalent to geodesics in the geometric sense.

We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a colloidal particle diffusing in a one dimensional harmonic potential. These protocols are verified numerically. We also calculate and numerically verify protocols optimizing the Hatano-Sasa Y-value (a quantity relevant for transitions between nonequilibrium steady states and similar to dissipated work) for a colloidal particle dragged through solution by a translating optical trap with two controllable parameters. Finally, in an application that has particular relevance to small-scale information processing systems, we calculate maximally efficient erasure cycles for deletion of a single classical bit of information. The system storing this bit consists of an overdamped Brownian colloidal particle diffusing in a one-dimensional double-well potential separated by a potential barrier stabilizing the memory.