Linear response theory and optimal control for a molecular system under non-equilibrium conditions

Abstract

In this paper, we propose a straightforward generalisation of the linear response theory on a finite time-horizon to systems in non-equilibrium that are subject to external forcing. We briefly revisit the standard linear response result for equilibrium systems, where we consider Langevin dynamics as a special case, and then give an alternative derivation using a change-of-measure argument that does not rely on any stationarity or reversibility assumption. This procedure easily enables us to calculate the second-order correction to the linear response formula (which may or may not be useful in practice). Furthermore, we outline how the novel non-equilibrium linear response formula can be used to compute optimal controls of molecular systems for cases in which one wants to steer the system to maximise a certain target expectation value. We illustrate our approach with simple numerical examples.