Optimal Control of Nonequilibrium Systems through Automatic Differentiation

Abstract

Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, in both nanotechnology and biology. Progress in computing optimal protocols to extremize thermodynamic variables has, thus far, been limited to either simple systems or near-equilibrium evolution. Here, we present an approach for computing optimal protocols based on automatic differentiation. Our methodology is applicable to complex systems and multidimensional protocols and is valid arbitrarily far from equilibrium. We validate our method by reproducing theoretical optimal protocols for a Brownian particle in a time-varying harmonic trap. We also compute departures from near-equilibrium behavior for magnetization reversal on an Ising lattice and for barrier crossing driven by a harmonic trap, which is used to represent a range of biological processes including biomolecular unfolding reactions. Algorithms based on automatic differentiation outperform the near-equilibrium theory for far-from-equilibrium magnetization reversal and for driven barrier crossing beyond the linear regime. The optimal protocol for far-from-equilibrium driven barrier crossing is found to hasten the approach to, and slow the departure from, the barrier region compared to the near-equilibrium theoretical protocol. We demonstrate the utility of our method in a real-world use case by reducing the work required to unfold a DNA hairpin in the coarse-grained oxDNA model and improving its nonequilibrium free-energy landscape reconstruction compared to a naive linear protocol.