Energetics of a simple microscopic heat engine

TL;DR

This paper models a microscopic heat engine using a particle on a lattice with thermal baths, deriving analytic expressions for its performance and comparing its efficiency to classical thermodynamic limits.

Contribution

It provides an analytic framework for a microscopic heat engine model and explores its operational regimes and efficiencies at different conditions.

Findings

Identifies regions where the system acts as a heat engine, refrigerator, or neither.

Derives steady-state current and heat flow expressions.

Shows efficiency approaches Carnot limits at quasistatic conditions.

Abstract

We model a microscopic heat engine as a particle hopping on a one-dimensional lattice in a periodic sawtooth potential, with or without load, assisted by the thermal kicks it gets from alternately placed hot and cold thermal baths. We find analytic expressions for current and rate of heat flow when the engine operates at steady state. Three regions are identified where the model acts either as a heat engine or as a refrigerator or as neither of the two. At quasistatic limit both efficiency of the engine and coefficient of performance of the refrigerator go to that for Carnot engine and Carnot refrigerator, respectively. We investigate efficiency of the engine at two operating conditions (at maximum power and at optimum value with respect to energy and time) and compare them with those of the endoreversible and Carnot engines.