Generalizing linear response to higher orders in minimal-work finite-time protocols

Linear response theory has been an extraordinarily useful tool for statistical physics. In stochastic thermodynamics, it has been used to compute minimal-work protocols that drive between thermodynamic states in finite time, valid for both slow-driving and weak-driving regimes. Here we review various linear-response-based approaches for calculating optimal protocols, and demonstrate how they may be derived from a more general Volterra Series functional expansion. This allows for a systematic construction of quadratic and higher-order response terms, which we use to make corrections to minimal-work protocols beyond the slow-driving and weak-driving regimes. We discuss the utility and tradeoffs of using higher-order terms to construct optimal protocols and illustrate our results for an analytic, overdamped particle in a harmonic trap.