Optimization of a class of heat engines with explicit solution

TL;DR

This paper analyzes a class of stochastic heat engines with explicit solutions, deriving key physical quantities and optimizing the external potential to enhance efficiency and power output.

Contribution

It provides explicit solutions for physical quantities of a specific class of heat engines and introduces an optimization method to improve their efficiency and power.

Findings

Explicit expressions for entropy, internal energy, work, and heat exchange.

Optimized external potential reduces irreversible work.

Calculated efficiencies at optimal conditions.

Abstract

A specific class of stochastic heat engines driven cyclically by time-dependent potential, which is defined in the half-line ($0<x<+\infty$), is analysed. For such engines, most of their physical quantities can be obtained explicitly, including the entropy and internal energy of the heat engine, as well as output work (power) and heat exchange with the environment during a finite time interval. The optimisation method based on the external potential to reduce {\it irreversible} work and increase energy efficiency is presented. With this optimised potential, efficiency $\eta^*$ and its particular value at maximum power $\eta^*_{\rm EMP}$ are calculated and discussed briefly.