Unattainability of Carnot efficiency in thermal motors: Coarse-graining and entropy production of Feynman-Smoluchowski ratchet

TL;DR

This paper investigates the thermodynamic efficiency limits of the Feynman-Smoluchowski ratchet, revealing hidden entropy productions due to coarse-graining, and proposes an extended stochastic thermodynamics framework to accurately account for dissipation.

Contribution

It introduces a method to reconstruct hidden entropy production in coarse-grained models of non-equilibrium systems, addressing a longstanding controversy.

Findings

Hidden entropy production exists in the FS ratchet due to coarse-graining.

Standard stochastic thermodynamics fails to capture all dissipation.

An extended framework can reconstruct hidden entropy production.

Abstract

We revisit and analyze the thermodynamic efficiency of the Feynman-Smoluchowski (FS) ratchet, a classical thought experiment describing an autonomous heat-work converter. Starting from the full kinetics of the FS ratchet and deriving the exact forms of the hidden dissipations resulting from coarse-graining, we restate the historical controversy over its thermodynamic efficiency. The existence of hidden entropy productions implies that the standard framework of stochastic thermodynamics applied to the coarse-grained descriptions fails in capturing the dissipative feature of the system. In response to this problem, we explore an extended framework of stochastic thermodynamics to reconstruct the hidden entropy production from the coarse-grained dynamics. The approach serves as a key example of how we can systematically address the problem of thermodynamic efficiency in a multi-variable fluctuating non-equilibrium system.