Underdamped stochastic heat engine at maximum efficiency

TL;DR

This paper analyzes the efficiency of an underdamped stochastic heat engine, deriving optimal protocols and revealing universal efficiency behaviors at maximum power and zero power, with implications for engine performance optimization.

Contribution

It provides an analytical framework for maximizing efficiency in underdamped stochastic heat engines and uncovers universal efficiency relations at different operational regimes.

Findings

Maximum efficiency aligns with Carnot at zero power.

Efficiency at maximum power matches Curzon-Ahlborn in weak damping.

Small deviations from maximum power can significantly increase efficiency.

Abstract

We investigate the performance of an underdamped stochastic heat engine for a time-dependent harmonic oscillator. We analytically determine the optimal protocol that maximizes the efficiency at fixed power. The maximum efficiency reduces to the Curzon-Ahlborn formula at maximum power and the Carnot formula at zero power. We further establish that the efficiency at maximum power is universally given by the Curzon-Ahlborn efficiency in the weakly damped regime. Finally, we show that even small deviations from operation at maximum power may result in a significantly increased efficiency.