Exploring the operation of a tiny heat engine

TL;DR

This paper models a tiny heat engine using a Brownian particle in a sawtooth potential with hot and cold baths, deriving steady state currents and analyzing its thermodynamic performance and operational regimes.

Contribution

It provides a closed-form expression for the steady state current and explores the conditions under which the model acts as a heat engine, refrigerator, or neither.

Findings

Identified parameter regions where the system functions as a heat engine or refrigerator.

Derived explicit formulas for steady state current and efficiency.

Mapped phase diagrams showing operational regimes.

Abstract

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by $\it {alternately}$ placed hot and cold heat baths along its path. We find closed form expression for the steady state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters of interest. When we plot the phase diagrams showing the way the model operates, we not only find regions where it functions as a heat engine and as a refrigerator but we also identify a region where the model functions as neither of the two.