Enhanced Efficiency in Shear-Loaded Brownian Gyrators

TL;DR

This paper explores how applying shear flow to a Brownian gyrator enhances its efficiency as a microscopic heat engine, approaching Carnot efficiency, but also introduces stability challenges.

Contribution

It analytically demonstrates that shear flow can significantly boost the efficiency of a Brownian gyrator as a heat engine and reveals a trade-off between efficiency and stability.

Findings

Efficiency approaches Carnot limit at maximum power with shear.

Shear flow enables the system to operate as a heat engine or refrigerator.

System stability may be compromised before reaching maximum efficiency.

Abstract

A Brownian gyrator is a system in which a particle experiences thermal noise from two distinct heat baths. This nonequilibrium setup inherently generates a nonzero torque, leading to gyrating motion around a potential energy minimum. As a minimal model for a heat engine, the Brownian gyrator provides valuable insights into energy conversion and nonequilibrium dynamics. Here, we investigate the effect of an externally imposed shear flow on a Brownian gyrator, treating it as a mechanical load. The shear flow introduces a tunable mechanism that allows the system to operate either as a heat engine, extracting work from the temperature gradient, or as a refrigerator, transferring heat from the colder to the hotter bath. Focusing on the heat engine regime, we analytically derive the steady-state probability distribution to compute the average torque exerted by the gyrator and quantify the mechanical power extracted from the shear. Our results show a remarkable increase in efficiency compared to the standard Brownian gyrator without shear, approaching Carnot efficiency at maximum power. Surprisingly, we also find that while the system can operate efficiently as a heat engine, it may become unstable before reaching the stall condition, highlighting a fundamental trade-off between efficiency and stability in shear-driven microscopic engines.