Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperature

TL;DR

This paper investigates the energetics of a Brownian heat engine and refrigerator driven by position-dependent temperature using numerical simulations, revealing differences from overdamped models and limited efficiency improvements.

Contribution

It provides a detailed numerical analysis of the inertial Langevin dynamics of Brownian engines with non-uniform temperature, highlighting the impact of kinetic energy entropy production.

Findings

Optimal parameters for performance identified

Efficiency lower than endoreversible engines in linear response

Potential and temperature profile optimization yields marginal gains

Abstract

The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the B\"uttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter values for optimal performance of the heat engine and heat pump. Our results qualitatively differ from approaches based on the overdamped model. The behavior of the heat engine and heat pump, in the linear response regime is examined under finite time conditions and we find that the efficiency is lower than that of an endoreversible engine working under the same condition. Finally, we investigate the role of different potential and temperature profiles to enhance the efficiency of the system. Our simulations show that optimizing the potential and temperature profile leads only to a marginal enhancement of the system performance due to the large entropy production via the Brownian particle's kinetic energy.