Kim, E-J and Hollerbach, R (2017) Signature of nonlinear damping in geometric structure of a nonequilibrium process. Physical Review E, 95 (2). 022137. ISSN 2470-0045
Abstract
We investigate the effect of nonlinear interaction on the geometric structure of a non-equilibrium process. Specifically, by considering a driven-dissipative system where a stochastic variable x is damped either linearly (∝ x) or nonlinearly (∝ x³) while driven by a white noise, we compute the time-dependent probability density functions (PDFs) during the relaxation towards equilibrium from an initial non-equilibrium state. From these PDFs, we quantify the information change by the information length L, which is the total number of statistically distinguishable states which the system passes through from the initial state to the final state. By exploiting different initial PDFs and the strength D of the white noise forcing, we show that for a linear system, L increases essentially linearly with an initial mean value yₒ of x as L ∝ yₒ, demonstrating the preservation of a linear geometry. In comparison, in the case of a cubic damping, L has a power-law scaling as L ∝ ym₀, with the exponent m depending on D and the width of the initial PDF. The rate at which information changes also exhibits a robust power-law scaling with time for the cubic damping.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017, American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Feb 2017 12:50 |
Last Modified: | 28 Sep 2022 19:53 |
Published Version: | https://doi.org/10.1103/PhysRevE.95.022137 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.95.022137 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112141 |