Minimal dissipation in processes far from equilibrium

TL;DR

This paper demonstrates that linear response theory can effectively identify minimal dissipation protocols in far-from-equilibrium thermodynamic processes, simplifying the optimization of energy-efficient driving strategies.

Contribution

It shows that linear response theory can predict optimal control protocols with step and delta-peak features, even far outside its usual validity range.

Findings

Optimal protocols exhibit step and delta-peak structures.

Linear response theory simplifies the derivation of optimal controls.

Applicability extends beyond the theory's traditional limits.

Abstract

A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control strategies are mathematically involved, and contain peculiar and counter-intuitive features. We show that optimal driving protocols determined by means of linear response theory exhibit the same step and $\delta$-peak like structures that were previously found from solving the full optimal control problem. However, our method is significantly less involved, since only a minimum of a quadratic form has to be determined. In addition, our findings suggest that optimal protocols from linear response theory are applicable far outside their actual range of validity.