Exact Time-Dependent Solutions and Information Geometry of a Rocking Ratchet

Eun-jin Kim, R. Hollerbach

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
45 Downloads (Pure)

Abstract

The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency.
Original languageEnglish
Article number314
Number of pages18
JournalSymmetry
Volume14
Issue number2
DOIs
Publication statusPublished - 3 Feb 2022

Bibliographical note

This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license (https://
creativecommons.org/licenses/by/4.0/).

Keywords

  • symmetry-breaking
  • over-damped complex system
  • Brownian ratchet
  • non-equilibrium
  • noise
  • Fokker-planck equation
  • Information length
  • irreversibility

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