Work extremum principle: Structure and function of quantum heat engines

TL;DR

This paper analyzes quantum heat engines with two subsystems and baths at different temperatures, deriving bounds on efficiency, and showing how work extraction relates to engine size, power, and thermodynamic limits.

Contribution

It introduces a framework for optimizing quantum heat engine performance beyond near equilibrium, establishing efficiency bounds and linking engine size to work extraction at maximum efficiency.

Findings

Efficiency bounded by Curzon-Ahlborn and Carnot limits.

Finite power engines have well-defined temperatures and obey the second law.

Small engines can reach Carnot efficiency at zero power.

Abstract

We consider a class of quantum heat engines consisting of two subsystems interacting via a unitary transformation and coupled to two separate baths at different temperatures $T_h > T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value $1-\sqrt{T_c/T_h}$ and from above by the Carnot value $1-(T_c/T_h)$. The latter is reached|at finite power|for a macroscopic engine, while the former is achieved in the equilibrium limit $T_h\to T_c$. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.