Optimal performance of periodically driven, stochastic heat engines under limited control

TL;DR

This paper analyzes the limits of efficiency for periodically driven stochastic heat engines with limited control, showing that full control over the system's Hamiltonian is necessary to reach Carnot efficiency, especially in underdamped systems.

Contribution

The authors develop a framework quantifying how limited control affects heat engine performance, revealing universal bounds and the necessity of full Hamiltonian control for optimal efficiency.

Findings

Maximum efficiency depends on control over the full Hamiltonian.

Underdamped heat engines cannot reach Carnot efficiency due to kinetic energy control limitations.

Universal one-parameter dependence of efficiency and power at maximum performance.

Abstract

We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.