### Abstract

Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.

Original language | English |
---|---|

Article number | 574 |

Journal | Entropy |

Volume | 20 |

Issue number | 8 |

DOIs | |

Publication status | Published - 3 Aug 2018 |

Externally published | Yes |

### Fingerprint

### Keywords

- Attractor
- Chaos
- Fisher information
- Fokker-Planck equation
- Information length
- Langevin equation
- Probability density function
- Relaxation
- Stochastic processes

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Investigating information geometry in classical and quantum systems through information length.** / Kim, Eun Jin.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Investigating information geometry in classical and quantum systems through information length

AU - Kim, Eun Jin

PY - 2018/8/3

Y1 - 2018/8/3

N2 - Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.

AB - Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathematical tool that is not specific to a particular system. We provide such a tool based on information geometry by quantifying the similarity and disparity between Probability Density Functions (PDFs) by a metric such that the distance between two PDFs increases with the disparity between them. Specifically, we invoke the information length L(t) to quantify information change associated with a time-dependent PDF that depends on time. L(t) is uniquely defined as a function of time for a given initial condition. We demonstrate the utility of L(t) in understanding information change and attractor structure in classical and quantum systems.

KW - Attractor

KW - Chaos

KW - Fisher information

KW - Fokker-Planck equation

KW - Information length

KW - Langevin equation

KW - Probability density function

KW - Relaxation

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85052225130&partnerID=8YFLogxK

U2 - 10.3390/e20080574

DO - 10.3390/e20080574

M3 - Article

VL - 20

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 8

M1 - 574

ER -