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Fisher and Shannon Functionals for Hyperbolic Diffusion
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  • Release Date: 2024-08-05
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Playlist
  • hyperbolic diffusion
  • telegrapher’s equation
  • Shannon entropy
  • Fisher information
  • Cramer-Rao bound
Video Introduction

This video is adapted from 10.3390/e25121627

The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the telegrapher’s equation. In the framework of hyperbolic diffusion, the non-local Fisher’s information with the x-parameter is related to the local Fisher’s information with the t-parameter. A perturbation theory is presented to calculate Shannon’s entropy of the telegrapher’s equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times).

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