Kim, E. (2016) Geometric structure and geodesic in a solvable model of nonequilibrium process. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 93 (6). 62127. ISSN 1539-3755
Abstract
We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process), we compute the time-dependent probability density functions (PDFs) and investigate the evolution of this system in a statistical metric space where the distance between two points (the so-called information length) quantifies the change in information along a trajectory of the PDFs. In this metric space, we find a geodesic for which the information propagates at constant speed, and demonstrate its utility as an optimal path to reduce the total time and total dissipated energy. In particular, through examples of physical realizations of such geodesic solutions satisfying boundary conditions, we present a resonance phenomenon in the geodesic solution and the discretization into cyclic geodesic solutions. Implications for controlling population growth are further discussed in a stochastic logistic model, where a periodic modulation of the diffusion coefficient and the deterministic force by a small amount is shown to have a significant controlling effect.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 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: | 01 Jul 2016 11:04 |
Last Modified: | 30 Nov 2016 13:05 |
Published Version: | https://dx.doi.org/10.1103/PhysRevE.93.062127 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevE.93.062127 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:101404 |