Multidimensional Minimum-Work Protocols

In this chapter, control protocols are designed that invert the magnetization of a \(3 \times 3\) Ising model with minimal energetic cost in the slow-driving limit and compared with naive protocols. Using multiple control parameters, which provide additional flexibility in manipulating the system conformation relative to a single control parameter, allows the system to be driven along a fast-relaxing pathway between reaction endpoints. An accounting of the work done by each control parameter is also presented and analyzed (Material in this chapter also appears in Ref. Louwerse and Sivak, J. Chem. Phys. 156:194108, 2022).