Kim, E. 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 nonequilibrium 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 nonequilibrium 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 y0 of x as L ∝ y0, demonstrating the preservation of a linear geometry. In comparison, in the case of a cubic damping, L has a power-law scaling as L ∝ ym 0 , 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 |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2017 American Physical Society. This is an author produced version of a paper subsequently published in Physical Review E. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Mar 2017 14:08 |
Last Modified: | 26 Mar 2018 22:23 |
Published Version: | https://doi.org/10.1103/PhysRevE.95.022137 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevE.95.022137 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113074 |