### 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 language | English |
---|---|

Article number | 062127 |

Journal | Physical Review E |

Volume | 93 |

Issue number | 6 |

DOIs | |

Publication status | Published - 20 Jun 2016 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E*,

*93*(6), [062127]. https://doi.org/10.1103/PhysRevE.93.062127

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

Research output: Contribution to journal › Article

*Physical Review E*, vol. 93, no. 6, 062127. https://doi.org/10.1103/PhysRevE.93.062127

}

TY - JOUR

T1 - Geometric structure and geodesic in a solvable model of nonequilibrium process

AU - Kim, Eun Jin

AU - Lee, Unjin

AU - Heseltine, James

AU - Hollerbach, Rainer

PY - 2016/6/20

Y1 - 2016/6/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84975298020&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.93.062127

DO - 10.1103/PhysRevE.93.062127

M3 - Article

VL - 93

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 6

M1 - 062127

ER -