Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

TL;DR

This paper derives the efficiency at maximum power for stochastic heat engines with Carnot-like, Stirling-like, and Ericsson-like cycles, using a Brownian particle model and low dissipation assumptions.

Contribution

It introduces a method to calculate efficiency at maximum power for mesoscopic stochastic engines with different cycle types using Langevin dynamics and finite-time thermodynamics.

Findings

Efficiency at maximum power derived for different cycle types

Model based on Brownian particle in harmonic potential

Application of low dissipation framework

Abstract

This work obtains the efficiency at maximum power for a stochastic heat engine performing Carnot-like, Stirling-like and Ericsson-like cycles. For the mesoscopic engine a Brownian particle trapped by an optical tweezers is considered. The dynamics of this stochastic engine is described as an overdamped Langevin equation with a harmonic potential, whereas is in contact with two thermal baths at different temperatures, namely, hot ($T_h$) and cold ($T_c$). The harmonic oscillator Langevin equation is transformed into a macroscopic equation associated with the mean value $\langle x^2(t)\rangle$ using the original Langevin approach. At equilibrium stationary state this quantity satisfies a state-like equation from which the thermodynamic properties are calculated. To obtained the efficiency at maximum power it is considered the finite-time cycle processes under the framework of low dissipation approach.