# Optimal discrete control: minimizing dissipation in discretely driven nonequilibrium systems

## TL;DR

This paper develops a theoretical framework to quantify and minimize energy dissipation in systems driven by discrete, instantaneous perturbations, with applications to molecular machines and nonequilibrium systems.

## Contribution

It generalizes existing results to include finite-time, discrete control protocols and provides a method to design minimum-dissipation control strategies.

## Key findings

- Derived the energetic cost of discrete, instantaneous driving out of equilibrium.
- Compared theoretical formalism with an exactly solvable model system.
- Demonstrated dissipation reduction in a multistable molecular machine model.

## Abstract

Microscopic machines utilize free energy to create and maintain out-of-equilibrium organization in virtually all living things. Often this takes the form of converting the free energy stored in nonequilibrium chemical potential differences into useful work, via a series of reactions involving the binding, chemical catalysis, and unbinding of small molecules. Such chemical reactions occur on timescales much faster than the protein conformational rearrangements they induce. Here, we derive the energetic cost for driving a system out of equilibrium via a series of such effectively instantaneous (and hence discrete) perturbations. This analysis significantly generalizes previously established results, and provides insight into qualitative, as well as quantitative, aspects of finite-time, minimum-dissipation discrete control protocols. We compare our theoretical formalism to an exactly solvable model system and also demonstrate the dissipation reduction achievable in a simple multistable model for a discretely driven molecular machine.