Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Theoretical Analysis of the Integral 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)

How to cite: Lokare, Y. A Theoretical Analysis of the Integral Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints 2021, 2021070686 (doi: 10.20944/preprints202107.0686.v1). Lokare, Y. A Theoretical Analysis of the Integral Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints 2021, 2021070686 (doi: 10.20944/preprints202107.0686.v1).

Abstract

A quantitative description of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of ideal colloidal systems in accelerated frames of reference over long time scales.

Supplementary and Associated Material

https://github.com/YashLokare02/Supplementary_information_IFT_colloidal_systems: GitHub repository that hosts the simulation codes used for numerical analysis

Keywords

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

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