Higher-order response theory in optimal stochastic thermodynamics

TL;DR

This paper explores higher-order response theory in stochastic thermodynamics, showing that including these terms offers limited practical benefit and can lead to unphysical predictions, despite increased computational complexity.

Contribution

It develops a framework for higher-order response in optimal stochastic thermodynamics and evaluates its effectiveness compared to linear response approximations.

Findings

Higher-order response terms can predict unphysical negative excess work.

Including higher-order responses offers marginal improvements in protocol optimization.

Higher computational cost may outweigh benefits of higher-order response inclusion.

Abstract

Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered nanoscale systems and understanding biomolecular machines. We compare and explore the relationships between linear-response-based approximations used to study optimal protocols in different driving regimes by showing that they arise as controlled truncations of a general causal response (Volterra) expansion. We then construct higher-order response terms and discuss the drawbacks and utility of their inclusion. We illustrate our results for an overdamped particle in a harmonic trap, ultimately showing that the inclusion of higher-order response in calculating optimal protocols provides marginal improvement in effectiveness despite incurring a significant computational expense, while introducing the possibility of predicting arbitrarily low and unphysical negative excess work.