Geometric structure and geodesic in a solvable model of nonequilibrium process

Eun Jin Kim, Unjin Lee, James Heseltine, Rainer Hollerbach

Research output: Contribution to journalArticle

19 Citations (Scopus)

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.

Original languageEnglish
Article number062127
JournalPhysical Review E
Volume93
Issue number6
DOIs
Publication statusPublished - 20 Jun 2016
Externally publishedYes

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Solvable Models
Geometric Structure
Non-equilibrium
Geodesic
metric space
probability density functions
Probability density function
Ornstein-Uhlenbeck process
Metric space
logistics
Exactly Solvable Models
Ornstein-Uhlenbeck Process
Population Growth
Optimal Path
Logistic Model
Dissipative Systems
diffusion coefficient
Diffusion Coefficient
trajectories
Stochastic Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Geometric structure and geodesic in a solvable model of nonequilibrium process. / Kim, Eun Jin; Lee, Unjin; Heseltine, James; Hollerbach, Rainer.

In: Physical Review E, Vol. 93, No. 6, 062127, 20.06.2016.

Research output: Contribution to journalArticle

Kim, Eun Jin ; Lee, Unjin ; Heseltine, James ; Hollerbach, Rainer. / Geometric structure and geodesic in a solvable model of nonequilibrium process. In: Physical Review E. 2016 ; Vol. 93, No. 6.
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