Optimal Control in Stochastic Thermodynamics

TL;DR

This paper reviews recent theoretical progress in optimal control within stochastic thermodynamics, focusing on minimum-dissipation protocols, their properties, and potential applications to chemical and biological systems.

Contribution

It synthesizes advances in understanding minimum-dissipation control, connecting optimal-transport theory with thermodynamic protocols, and discusses approximate and numerical methods for practical implementation.

Findings

Exact solutions reveal properties of minimum-dissipation control.

Connections to optimal-transport theory provide bounds on dissipation.

Approximate methods effectively reproduce known solutions.

Abstract

We review recent progress in optimal control in stochastic thermodynamics. Theoretical advances provide in-depth insight into minimum-dissipation control with either full or limited (parametric) control, and spanning the limits from slow to fast driving and from weak to strong driving. Known exact solutions give a window into the properties of minimum-dissipation control, which are reproduced by approximate methods in the relevant limits. Connections between optimal-transport theory and minimum-dissipation protocols under full control give deep insight into the properties of optimal control and place bounds on the dissipation of thermodynamic processes. Since minimum-dissipation protocols are relatively well understood and advanced approximation methods and numerical techniques for estimating minimum-dissipation protocols have been developed, now is an opportune time for application to chemical and biological systems.