Feynman-Smoluchowski engine at high temperatures and the role of constraints

TL;DR

This paper investigates the Feynman-Smoluchowski ratchet as a heat engine at high temperatures, deriving universal efficiency results and exploring how constraints influence its thermodynamic performance.

Contribution

It derives the universality of efficiency at maximum power for the high-temperature limit and maps constrained linear models to finite-time thermodynamics.

Findings

Universal efficiency at maximum power up to second order.

Constraints lead to known finite-time thermodynamics efficiencies.

Linear constrained models can be mapped to effective thermodynamic models.

Abstract

Feynman's ratchet and pawl is a paradigmatic model for energy conversion using thermal fluctuations in the mesoscopic regime. Here, we optimize the power output of the ratchet as a heat engine in the high temperatures limit, and derive the universality of efficiency at maximum power up to second order, using a non-linear approximation. On the other hand, the linear model may be optimized by constraining the internal energy scales in different ways. It is shown that simple constraints lead to well-known expressions of thermal efficiency in finite-time thermodynamics. Thereby, the constrained ratchet, in the linear regime, has been mapped to an effective finite-time thermodynamic model.