An adjustable Brownian heat engine

TL;DR

This paper models a microscopic Brownian heat engine in a sawtooth potential, deriving explicit expressions for current, efficiency, and refrigerator performance, and analyzing optimal operating conditions and efficiencies compared to classical engines.

Contribution

It provides a closed-form analytical model of a Brownian heat engine with adjustable parameters, including conditions for maximum power and efficiency.

Findings

Derived explicit current and efficiency expressions.

Identified parameter regimes for maximum power and efficiency.

Compared engine efficiencies with Carnot and endoreversible engines.

Abstract

A microscopic heat engine is modeled as a Brownian particle in a sawtooh potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs either with maximum power or with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines.