Full Counting Statistics and Fluctuation Theorem for the Currents in the Discrete Model of Feynman's Ratchet

TL;DR

This paper analyzes the fluctuations of currents in a discrete Feynman's ratchet model, demonstrating the validity of fluctuation theorems, fluctuation-dissipation relations, and Onsager reciprocity through detailed statistical analysis.

Contribution

It provides a comprehensive study of current fluctuations, full counting statistics, and fluctuation theorems in a discrete Feynman's ratchet model, including numerical verification of fundamental relations.

Findings

Fluctuation theorem holds for joint current distribution.

Fluctuation-dissipation and Onsager relations are numerically satisfied.

Identified two macroscopic currents with their affinities.

Abstract

We provide a detailed investigation on the fluctuations of the currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also investigate full counting statistics of the two currents and show that fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.