Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit

Version 1 : Received: 29 July 2021 / Approved: 30 July 2021 / Online: 30 July 2021 (09:24:02 CEST)
Version 2 : Received: 13 April 2022 / Approved: 13 April 2022 / Online: 13 April 2022 (13:54:12 CEST)
Version 3 : Received: 3 June 2022 / Approved: 6 June 2022 / Online: 6 June 2022 (09:14:36 CEST)
Version 4 : Received: 8 June 2022 / Approved: 9 June 2022 / Online: 9 June 2022 (10:48:18 CEST)
Version 5 : Received: 4 July 2022 / Approved: 5 July 2022 / Online: 5 July 2022 (13:40:14 CEST)

How to cite: Lokare, Y. A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints 2021, 2021070686. https://doi.org/10.20944/preprints202107.0686.v2 Lokare, Y. A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints 2021, 2021070686. https://doi.org/10.20944/preprints202107.0686.v2

Abstract

A quantitative description of the second law of thermodynamics in small scale systems and over short time scales comes from various fluctuation theorems. The applicability of the transient fluctuation theorem in particular to small scale systems perturbed from an initial equilibrium steady-state distribution has been demonstrated both theoretically and experimentally in several works over the past few decades. In addition, some experimental works in the past have also made successful attempts to demonstrate the applicability of the fluctuation theorem to small scale systems evolving from a certain nonequilibrium steady-state distribution over relatively long time scales. To this end, this paper seeks to demonstrate the transient fluctuation theorem for a Brownian particle confined within a power-law trapping potential by following the trajectory of the particle that itself is translating linearly along one dimension with constant acceleration in a viscous fluid. Considered herein is an idealized version of this model, in that it is assumed that the force of the trapping potential is only felt by the translating Brownian particle confined within the trap, and that this Brownian particle moves relative to the fluid molecules that are held stationary. The results presented herein show that the transient fluctuation theorem applies not only to equilibrium steady-state distributions but also to nonequilibrium steady-state distributions of an ideal colloidal system in an accelerated frame of reference in the asymptotic (long-time) limit.

Supplementary and Associated Material

https://doi.org/10.5281/zenodo.5573326: Simulation codes deposited at Zenodo

Keywords

Time-reversed trajectory; colloidal systems; integral fluctuation theorem; dissipation function; power-law traps

Subject

Physical Sciences, Atomic and Molecular Physics

Comments (1)

Comment 1
Received: 13 April 2022
Commenter: Yash Lokare
Commenter's Conflict of Interests: Author
Comment: Additional statistical analyses have been performed and the results included herein. The title has been modified slightly to suit the narrative of the article. Numerical results have been updated and included herein. Analytical results have been updated and included herein as well. 
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