### 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 |
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Article number | 574 |

Journal | Entropy |

Volume | 20 |

Issue number | 8 |

DOIs | |

Publication status | Published - 3 Aug 2018 |

Externally published | Yes |

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### 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)