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. Preprints2021, 2021070686. https://doi.org/10.20944/preprints202107.0686.v3
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.v3
Lokare, Y. A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints2021, 2021070686. https://doi.org/10.20944/preprints202107.0686.v3
APA Style
Lokare, Y. (2022). A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit. Preprints. https://doi.org/10.20944/preprints202107.0686.v3
Chicago/Turabian Style
Lokare, Y. 2022 "A Theoretical Analysis of the Transient Fluctuation Theorem for Accelerated Colloidal Systems in the Long-Time Limit" Preprints. https://doi.org/10.20944/preprints202107.0686.v3
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.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
6 June 2022
Commenter:
Yash Lokare
Commenter's Conflict of Interests:
Author
Comment:
A test for the validity of the TFT was left incomplete in version 2 of the article. To this end, 4 more plots have been added (i.e., Figs. 5, 6, 10, and 11) to provide an exhaustive test of the TFT for both, the harmonic trap and quartic confining potential cases, respectively. A straightforward deduction of the TFT from Eq. 27 has also been included in the article. Additional numerical results have been added as well (i.e., extracted slopes of the lines of best fit in Figs. 5, 6, 10, and 11).
Commenter: Yash Lokare
Commenter's Conflict of Interests: Author