Optimal thermodynamic control in open quantum systems

TL;DR

This paper develops control theory methods to optimize thermodynamic processes in open quantum systems, leading to strategies that maximize work output and minimize heat dissipation, with explicit solutions for two-level systems.

Contribution

It introduces a novel control framework for optimizing thermodynamic performance in open quantum systems, including bang-bang solutions and explicit analysis for two-level heat engines.

Findings

Optimal control strategies are characterized by bang-bang solutions.

Maximum power is linked to a conserved quantity in the control problem.

Explicit optimal cycle and efficiency are derived for a two-level heat engine.

Abstract

We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes which minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.